WIND  STRESSES 


[FLEMING] 


Six  Jyfono&ra  pAr  on 

~./-    ,    —v'    / 

Wind 


WIND  PRESSURE  FACTORS 
SPECIFICATION  REQUIREMENTS 
MILL-BUILDING  STRESSES 
RIGID  JOINT  •  WIND  BRACING 
FOR  OFFICE  BUILDINGS 


BY  ROBINS  FLEMING 
Engineer,  American  Bridge  Company ,  New  York 


REVISED  AND  ENLARGED  REPRINTS  FROM 
ENGINEERING  NEWS 


ENGINEERING  NEWS 

HILL  BUILDING,  NEW  YORK 

1915 


Copyright,  1915, 

by 
Hill  Publishing  Co. 


PREFACE 

Wind  is  everywhere.  It  affects  all  structures.  Every 
engineer,  or  even  every  person  who  ever  sees  an  engineer, 
has  a  personal  interest  in  the  effect  of  wind  on  structures. 
That  is  the  subject  of  the  present  book. 

Ignorance  is  not  always  bliss.  If  it  be  true — as  seems 
very  likely — that  wind  is  preeminently  a  matter  concern- 
ing which  no  one  knows  he  knows  not,  then  this  book 
deserves  to  have  many  readers. 

There  is  a  fresh  touch  to  what  the  author  says.  His 
main  argument  throughout  is  common  sense.  In  this 
respect  his  frame  of  mind  is  catching;  the  reader  will 
find  himself  saner  and  sounder  for  having  read  the  book. 
When  the  author  refers  to  intricate  studies  of  wind 
action,  claimed  to  show  the  need  for  radical  changes 
in  building  practice,  he  leads  us  to  notice  the  practical 
fact  that  these  intricate  studies  are  based  on  tests  made 
in  mild  breezes,  and  can  hardly  be  safe  guides  as  to 
what  happens  in  storms. 

Six  articles  which  appeared  in  ENGINEERING  NEWS, 
most  of  them  in  the  early  months  of  1915,  make  up 
this  book.  One  of  the  six,  however — No.  6 — is  so 
changed  from  the  form  in  which  it  was  printed  March 
13,  1913,  that  it  is  new.  And  this  subject,  the  stress 
calculation  for  tier-building  frames  without  diagonals,  is 
so  far  without  any  literature. 

The  many  slow  hours  of  work  which  the  author  con- 
sumed in  searching  out  and  studying  the  material  re- 
quired for  writing  this  book  merit  the  reader's  apprecia- 
tion. 

EDITOE  Engineering  News. 


382055 


CONTENTS 

Page 

I    Wind  Pressure  Formulas  and  Their  Experi- 
mental Basis 

II    Wind  Stresses  in  Steel  Mill  Buildings  .      .  13 

III  Wind  Stresses  in  Eailroad  Bridges  •      •      •  ^7 

IV  Wind  Stresses  in  Highway  Bridges  .      .      . 

V    Windbracing    Kequirements    in    Municipal 

Building     Codes 53 

VI    Windbracing  without  Diagonals  for   Steel- 
Frame   Office  Buildings 61 


Wind  Pressure  Formulas  and 
Their  Experimental  Basis 

SYNOPSIS — A  discussion  of  the  current  formu- 
las for  relation  between  wind  pressure  and  velocity, 
relation  between  pressure  on  normal  planes  and 
planes  inclined  to  the  wind,  and  several  other 
phases  of  wind  pressure.  The  author  brings  out 
strikingly  how  inadequate  is  the  experimental  basis 
for  the  formulas  and  figures  commonly  employed. 

The  purpose  of  this  article  is  to  give  the  basis  from 
which  some  of  the  commonly  used  formulas  for  wind 
pressure  are  derived.  Even  the  engineer  who  wishes  to 
know  only  the  wind  pressure  in  pounds  per  square  foot 
for  which  he  shall  make  provision  in  his  structure  will  be 
better  equipped  for  designing  if  he  is  acquainted  with  the 
foundations  on  which  ordinary  practice  rests. 

KELATION  BETWEEN  WIND  PBESSUBE  AND  VELOCITY 

In  view  of  the  extent  of  the  literature  on  the  subject  it 
might  reasonably  be  supposed  that  the  elementary  prin- 
ciples of  wind  pressure  are  determined,  at  least  theoretic- 
ally. How  near  this  is  to  being  the  case  may  be  inferred 
from  the  following  extracts  taken  from  two  modern 
American  textbooks,  each  of  which  is  regarded  as  an 
authority.  Marburg,  in  his  Framed  Structures  and 
Girders,  under  ''Wind  Pressure,"  writes: 

Theoretically  the  pressure  p,  in  Ib.  per  sq.ft.,  on  a  plane 
surface  normal  to  the  direction  of  flow  of  a  fluid  having  a 
relative  velocity  v,  in  ft.  per  sec.,  is  equal  to  the  weight  of 
a  vertical  column  of  the  fluid  having  a  cross-section  of  1 
sq.ft.  and  a  height  h,  in  ft.  equal  to  that  through  which  a 
freely  moving  body  must  fall  to  acquire  the  velocity  v.  If 
w  denotes  the  weight  of  the  fluid,  in  Ib.  per  cu.ft., 

wv2 

p    =    Wh    =    _  (1, 

For  air  at  a  temperature  of  32°  F.  and  at  a  barometric 
pressure  of  760  mm.,  w  =  0.081.  Letting  g  =  32.2, 

p  =  0.00126  v«  (2) 

[i] 


If    V    denotes    the    velocity    of    the    wind    in    miles    per    hour, 
v  =.  1.47  V,  whence  equation  (2)  becomes 

p    —    0.0027V2  (3) 

Burr  and  Falk,  in  The  Design  and  Construction  of 
Metallic  Bridges,  under  "Stresses  due  to  Wind"  write: 

If  the  wind  were  directed  as  a  finite  stream  against  an 
infinitely  large  surface,  so  that  the  direction  of  the  air  is 
completely  changed,  an  equation  expressing  the  force  against 
that  surface  may  be  obtained  from  the  laws  of  mechanics. 
Let 

W  ==  the    weight    of    air    directed    against    any    normal 

surface  in  a  given  time; 

w  =  the  weight  in  pounds  of  one  cubic  foot  of  air; 
v  =  the  velocity  of  wind  in  feet  per  second; 
a  ==  the  area  of  cross-section  of  the  wind  stream, 

Then  W  =  wav. 
Let 

M  =  the   mass   of  air   of  the   weight  W; 
g  =  the    acceleration    due    to    gravity    =    32.2    feet    per 

second; 
P  =  the   force   acting   on   the  area  a, 

Wv          wava 

Then  F  =   Mv   =  =  (1) 

g  g 

If  a  be  taken  at  1  sq.ft.,  and  w  at  0.0807  Ib.  per  cu.ft.  for 
a  temperature  of  32°  F.  and  a  barometric  pressure  of  760 
mm.,  and  if  v  be  replaced  by  V,  the  velocity  in  miles  per 
hour,  then 

P    =    0.0054  V2  (2) 

The  reader  will  observe  that  starting  with  the  same  as- 
sumptions one  author  finds  the  resultant  pressure  to  be 
twice  that  of  the  other.  Both  authors  make  haste  to  write 
that  the  theoretical  conditions  upon  which  their  formula 
is*  based  do  not  exist.  A  cushion  of  air  is  formed  in  front 
of  the  plate  and  a  partial  vacuum  at  the  back ;  there  is  a 
certain  amount  of  air  friction  and  the  change  of  direction 
is  not  complete.  The  student  facing  such  conflicting 
theories  on  the  very  fundamentals  of  wind  pressure  may 
well  raise  the  question  of  authority. 

It  is  almost  impossible  to  give  undue  credit  to  Sir  Isaac 
Newton  for  his  work  in  the  realms  of  science  and  mathe- 
matics. His  great  book  was  the  Philosophia  Naturalis 
Principia  Mathematica,  or  "The  Mathematical  Principles 
of  Natural  Philosophy,"  commonly  called  the  Principia. 
Originally  published  in  1686,  revised  editions  were  is- 
sued in  1713  and  1726.  Modern  hydrodynamics  had  its 

[2] 


origin  in  the  second  book,  treating  of  Motion  of  Bodies  in 
Resisting  Mediums.  Section  VIII  of  this  book  is  entitled 
''Of  Motion  Propagated  through  Fluids."  A  translation 
of  Prop.  XLVIII  (Newton  wrote  in  Latin)  reads: 

The  velocities  of  pulses  propagated  in  an  elastic  fluid  are 
in  a  ratio  compounded  of  the  subduplicate  ratio  of  the  elastic 
force  directly,  and  the  subduplicate  ratio  of  the  density  in- 
versely; supposing-  the  elastic  force  of  the  fluid  to  be  pro- 
portional to  its  condensation. 


This  means  that  the  velocity  v  varies  as  -7—,  or  p  varies 

V  a 

as  dv2.  For  wind  pressure,  the  density  of  the  air  being 
constant,  we  have  the  law  that  the  pressure  varies  di- 
rectly as  the  square  of  the  velocity,  which  has  remained 
almost  undisputed  since  Newton's  day. 

Furthermore,  according  to  Newton,  for  an  area  of 

v2 
unity,  p  =  dh,  in  which  h  =  ^—  is  the  distance  through 

which  a  heavy  body  must  fall  to  acquire  the  velocity  v, 
g  being  the  coefficient  of  gravity  or  32.2.  This  may  be 
called  the  Newtonian  theory,  and  has  been  followed  by 
a  host  of  writers,  including  Marburg  (quoted  above). 

W.  J.  M.  Rankine  was  one  of  the  master  mathema- 
ticians of  the  nineteenth  century.  In  his  fifteenth  year 
his  uncle  presented  him  with  a  copy  of  Newton's  Prin- 
cipia,  which  he  read  carefully.  He  remarks,  "This  was 
the  foundation  of  my  knowledge  of  the  higher  mathe- 
matics, dynamics  and  physics."  But  the  pupil  did  not 
blindly  follow  the  master.  In  his  Applied  Mechanics, 
he  has  a  section  devoted  to  "Mutual  Impulse  of  Fluids 
and  Solids."  A  jet  of  fluid  A,  striking  a  smooth  sur- 
face, is  deflected  so  as  to  glide  along  the  surface  in  that 
path  which  makes  the  smallest  angle  with  its  original  di- 
rection of  motion.  Let  v  be  the  velocity  of  the  particle 
of  fluid,  q  the  volume  discharged  per  second  equal  to  Av, 
d  the  density,  and  0  the  angle  by  which  the  direction  of 

motion  is  deflected;  then  —  —  is  the  momentum  of  the 

y 

quantity  of  fluid  whose  motion  is  deflected  per  second. 
With  these  notations  the  general  equation  for  the  force 

[3] 


Fx  perpendicular  to  the  plane  in  question  is  found  to  be 


For  the  particular  case  of  the  plane  at  right  angles  to  the 
jet  or  B  =  90°, 


9  9 

This  may  be  called  the  impact  theory,  and  is  followed  in 
some  textbooks,  including  that  of  Burr  and  Falk. 

From  the  time  of  Newton  until  this  day  a  long  line  of 
investigators  have  sought  by  experiment  to  obtain  the 
value  of  Tc  in  the  formula  P  =  kV2f  in  which  P  =  pres- 
sure in  Ib.  per  sq.ft.  and  V  =  velocity  in  miles  per  hour. 
As  before  noted,  according  to  the  Newton  formula  Ic  is 
0.0027  and  with  the  same  assumptions  according  to  Ran- 
kine  Tc  is  0.0054.  What  is  known  as  the  Smeaton  for- 
mula held  almost  universal  sway  for  150  years  and  is  still 
in  use.  It  is  very  simple,  P  =  1/200  V2.  In  the  Philoso- 
phical Transactions  of  the  Royal  Society,  England,  for 
the  year  1759  is  a  lengthy  paper  entitled,  An  Experi- 
mental Enquiry  Concerning  the  Natural  Power  of  Water 
and  Wind  to  Turn  Mills,  and  Other  Machines,  Depend- 
ing on  a  Circular  Motion.  By  Mr.  J.  Smeaton,  F.  R.  8. 
Part  III  is  "On  the  Construction  and  Effects  of  Wind- 
mill-Sails/' For  his  experiments  Smeaton  constructed 
an  elaborate  machine  or  whirling-table  in  which  fixed 
sails  revolved  through  the  air  about  a  given  axis  and  their 
velocities  were  measured  by  the  weights  lifted.  A  foot- 
note reads: 

Some  years  ago  Mr.  Rouse,  an  ingenious  gentleman  of 
Hasborough  in  Leicestershire,  set  about  trying  experiments 
on  the  velocities  of  the  wind,  and  force  thereof  upon  plain 
surfaces  and  windmill  sails. 

It  is  presumed,  though  not  so  stated,  that  Mr.  Rouse 
used  a  whirling-table  similar  to  that  described  by 
Smeaton.  Further  on  in  the  paper  a  table  "containing 
the  velocity  and  force  of  wind,  according  to  their  common 

appellations,"  is  found  introduced  with  : 

The  following  table  which  was  communicated  to  me  by 
my  friend  Mr.  Rouse,  and  which  appears  to  have  been  con- 
structed with  great  care,  from  a  considerable  number  of 

[4] 


facts  and  experiments,  and  which  having  relation  to  the  sub- 
ject of  this  article;  I  here  insert  as  he  sent  it  to  me;  but  at 
the  same  time  must  observe  that  the  evidence  for  those  num- 
bers where  the  velocity  of  the  wind  exceeds  50  miles  an  hour,  do 
not  seem  of  equal  authority  with  those  of  50  miles  an  hour 
and  under.  It  is  also  to  be  observed,  that  the  numbers  in 
column  3  are  calculated  according  to  the  velocity  of  the 
wind,  which  in  moderate  velocities,  from  what  has  been  be- 
fore observed,  will  hold  very  nearly. 

From  this  introduction  it  is  impossible  to  tell  where  ex- 
periment ended  and  theory  began.  The  coefficient  of  V* 
according  to  the  figures  given  in  the  third  column  of  the 
table  is  found  to  be  0.00492,  or  V2oo  nearly.  It  is  hard 
to  understand  how  a  formula  resting  upon  such  a  slender 
foundation  should  have  had  such  wide  vogue. 

The  most  careful  experiments  of  recent  years  for  the 
pressure  on  flat  plates  of  moderate  size  normal  to  the  di- 
rection of  a  uniform  wind  give  a  value  of  Tc  from  0.0032 
tc  0.004.  Hence  the  formula  P  =  0.004  V2  may  be 
safely  used.  It  is  interesting  to  note  that  Weisbach,  in 
his  monumental  work,  the  Mechanics  of  Engineering, 
followed  Newton's  method  but  multiplied  the  value  of  Tc 
as  found  by  this  method  by  a  coefficient  1.86,  stating  that 
about  two-thirds  of  the  action  is  upon  the  front  and  about 
one-third  upon  the  rear  surface.  He  based  his  coefficient 
upon  the  experiments  of  Dubuat  (about  1780)  and  Thi- 
bault  (1826). 

The  U.  S.  Weather  Bureau  uses  the  formula 

P  =  0.004  ^-F2 
oO 

in  which  B  =  height  of  barometer  in  inches.  This  for  the 

Tt 

engineer  is  an  unnecessary  refinement  as  ^  varies  but 

oU 

little  from  unity.  Wolff  in  his  book  The  Windmill  as  a 
Prime  Mover  takes  into  account  also  the  effect  of  tem- 
perature in  determining  wind  pressure.  At  sea  level  for 
a  wind  velocity  of  40  miles  per  hour  he  finds  pressures 
of  8.6  Ib.  per  sq.ft.  for  0°  F.  to  7.08  Ib.  for  100°  F.  For 
a  velocity  of  80  miles  per  hour  he  finds  pressures  of 
34.98  Ib.  per  sq.ft.  at  0°  F.  to  28.86  Ib.  at  100°  F. 
WIND-PRESSURE  COEFFICIENT  FOR  INCLINED  SURFACES 
For  the  intensity  of  wind  pressure  on  inclined  surfaces 
we  have  a  wide  range  of  values  from  which  to  choose. 

[  5  ] 


Tiberius  Cavallo,  F.  E.  S.,  etc.,  in  1803,  published  a  four- 
volume  treatise  on  The  Elements  of  Natural  or  Experi- 
mental Philosophy.  The  writer  has  never  seen  the  treatise 
quoted,  but  Chapter  IV  of  Book  II,  "Of  the  Action  of 
^"onelastic  Fluids  in  Motion,"  and  Chapter  X  of  the  same 
book,  "Of  Air  in  Motion,  or  of  the  Wind,"  are  written 
in  a  truly  scientific  spirit  and  are  readable  today.  A 
proposition  of  Cavallo's  reads,  "The  forces  of  a  fluid 
medium  on  a  plane  cutting  the  direction  of  its  motion 
with  different  inclinations  successively,  are  as  the  square? 
of  the  sines  of  these  inclinations."  This,  however,  ia 
implied  by  the  great  Newton  in  the  Principia,  Book  II, 
Prop.  XXXIV.  Among  recent  writers  Spofford  in  "The 
Theory  of  Structures"  deduces  the  same  theoretical  re- 
sults. 

As  these  results  differ  widely  from  those  obtained  by 
experiment,  recourse  must  be  had  to  empirical  formulas. 
Among  such,  Button's  formula  has  been  used  in  England 
and  the  United  States  perhaps  more  than  all  others  com- 
bined. It  is  still  found  in  the  latest  editions  of  many 
technical  books.  The  experiments  upon  which  it  is  based 
were  decidedly  crude.  Tract  XXXVI  of  Tracts  on 
Mathematical  and  Philosophical  Subjects  by  Charles 
Hutton,  LL.D.,  F.E.S.,  Professor  of  Mathematics  in  the 
Eoyal  Military  Academy  of  Woodwich,  England,  entitled, 
"Eesistance  of  the  Air  Determined  by  the  Whirling- 
Machine,"  records  his  experiments.  Hutton  secured  a 
whirling-machine  and  during  1786  and  1787  experi- 
mented with  hemispheres  and  cones.  Under  date  of  July 
23,  1788,  he  records: 

Prepared  the  machine  to  make  experiments  with  figures 
of  shapes  different  from  the  foregoing  ones.  Procuring  a 
thin  rectangular  plate  of  brass  to  fix  on  the  arm  of  the  ma- 
chine; its  weight  11^  oz.  and  its  dimensions  8  in.  by  4  in., 
consequently  its  area  was  32  sq.in.  ...  It  was  adapted 
for  fitting  on  the  end  of  the  arm  in  both  directions,  .  .  . 
It  was  also  contrived  to  incline  the  surface  in  any  degree 
to  the  direction  of  motion,  to  try  the  resistance  at  all  angles 
of  inclination.  When  fitted  on  with  its  length  in  the  direction 
of  its  arm,  the  distance  of  its  center  from  the  axis  of  mo- 
tion was  53%  in.;  and  the  same  distance  also  when  fitted  on 
the  other  way. 

Experiments  were  carried  on  at  different  inclinations 
of  plate  with  a  velocity  of  12  ft.  per  sec.  or  8.2  miles  per 

[6] 


hour.  When  attempting  to  bring  the  velocity  up  to  20 
ft.  per  sec.  or  13.6  miles  per  hour,  the  thread  carrying 
the  weight  broke.  These  experiments  are  recorded  under 
dates  of  July  24,  25,  31  and  Aug.  11.  The  results  ob- 
tained were  tabulated  and  the  well  known  formula 
Pn  =  P  (sitfx)l-**co*x-i 

was  deduced.    This  is  sometimes  called  Unwin's  formula, 
though  for  what  reason  is  not  clear,  as  Prof.  Unwin 
simply  quotes  Prof.  Hutton's  formula  approvingly. 
The  Duchemin  formula 

P         p    2  sin  A 
1  +  sin*  A 

for  inclined  surfaces  may  be  said  to  represent  the  best 
knowledge  on  the  subject  and  is  considered  the  most  re- 
liable formula  in  use.  The  pressures  obtained  are  greater 
than  those  from  the  Hutton  formula.  Col.  Duchemin,  a 
French  army  officer,  made  his  investigations  in  1829  and 
the  results  were  published  in  1842  (Bixby).*  Consider- 
able weight  has  been  attached  to  the  work  of  Col.  Duche- 
min. Weisbach  quotes  it,  as  well  as  most  writers  since 
his  time.  The  Duchemin  formula  was  verified  by  S.  P. 
Langley  in  1888.  He  had  erected  at  the  Allegheny 
(Penn.)  Observatory  a  whirling-table  consisting  of  two 
symmetrical  wooden  arms,  each  30  ft.  long,  revolving  in 
a  plane  8  ft.  above  the  ground.  The  motion  thus  ob- 
tained was  nearly  rectilinear,  quite  in  contrast  with  that 
from  Button's  machine  of  less  than  5-ft.  radius.  He  also 
used  velocities  up  to  100  ft.  per  sec.,  or  nearly  70  miles 
per  hour.  He  writes: 

At  the  inception  of  the  experiments  with  this  apparatus 
it  was  recognized  that  the  Newtonian  law,  which  made  the 
pressure  on  an  inclined  surface  proportional  to  the  square 
of  the  sine  of  the  angle,  was  widely  erroneous.  Occasional 
experiments  have  been  made  since  the  time  of  Newton  to 
ascertain  the  ratio  of  the  pressure  upon  a  plane  inclined  at 
various  angles  to  that  upon  a  normal  plane,  but  the  published 

*The  writer,  while  obtaining  his  information  first  hand 
from  the  sources  quoted,  acknowledges  an  obligation  to  a 
valuable  report:  Appendix  C  of  the  Report  of  Sept.  29,  1894, 
of  the  Special  Army  Engineer  Board  as  to  the  Maximum  Span 
Practicable  for  Suspension  Bridges.  By  W.  H.  Bixby,  Captain 
(now  General)  of  Engineers,  U.  S.  A.  It  is  really  a  treatise 
on  wind  pressure  in  engineering  construction.  It  is  said  only 
500  copies  were  issued.  This  valuable  paper  may  be  found 
reprinted  entire  in  "Engineering  News,"  Mar.  14,  1895. 


experiments  exhibit  extremely  wide  discordance,  and  a  series 
of  experiments  upon  this  problem  seemed  therefore,  to  be 
necessary  before  taking  up  some  newer  lines  of  inquiry. 

It  is  remarkable  that  Langley  obtained  results  varying 
less  than  3%  from  those  derived  from  the  Duchemin  for- 
mula. Regarding  this  he  writes : 

Only  since  making  these  experiments  my  attention  has 
been  called  to  a  close  agreement  of  my  curve  with  the 
formula  of  Duchemin,  whose  valuable  memoir  published  by 
the  French  War  Department,  "Memorial  de  1'Artillerie"  No. 
V,  I  regret  not  knowing  earlier. 

Attention  is  called  to  the  monographs  by  Langley, 
Experiments  in  Aerodynamics  and  The  Internal  Worlc 
of  the  Wind,  being  Numbers  801  and  884  of  the  "Smith- 
sonian Contributions  to  Knowledge." 

WIND  PEESSUKE  ON  NONPLANAR  SURFACES 

When  the  wind  blows  on  nonplanar  surfaces  the  pres- 
sure on  the  projected  area  depends  upon  the  form  of  the 
surface.  This  is  important  in  the  case  of  the  cylinder 
(standpipes,  chimneys  and  similar  objects).  Rankine 
states  in  his  Applied  Mechanics,  "The  total  pressure  of 
the  wind  against  the  side  of  a  cylinder  is  about  one-half 
of  the  total  pressure  against  a  diametral  plane  of  that 
cylinder."  A  theoretical  value  of  two-thirds  is  found  in 
some  treatises,  but  in  engineering  practice  one-half  is 
generally  used. 

Goodman  in  his  Mechanics  Applied  to  Engineering, 
London,  1904,  gives  the  following  ratios  of  pressure: 

Plat  plate  1.0 

Sphere  0.36  to  0.41 

Elongated    projectile  0.5 

Cylinder  0.54  to  0.57 

Wedge    (base    to   wind)  0.8    to  0.97 

Wedge    (edge  to  wind)  0.6    to  0.7 

Vertex   angle    90° 

Cone    (base    to    wind)  0.95 
Cone    (apex  to  wind) 

Vertex    angle    90°  0.69  to  0.72 

Vertex    angle    60°  0.54 

Lattice    girders    about  0.8 

WIND  PRESSURE  ON  PARALLEL  PLATES 
The  pressures  upon  parallel  plates  or  bars  with  an  open 
space  between  them  are  important  in  application  to  plate- 
girder  bridges,  the  trusses  in  a  truss  bridge,  or  parallel 
bars  in  the  same  truss  when  one  bar  is  behind  another. 

[8] 


The  Committee  of  the  National  Physical  Laboratory, 
England,  having  decided  that  one  of  the  first  researches 
to  be  undertaken  in  the  Engineering  Laboratory  should 
be  the  investigation  of  the  distribution  and  intensity  of 
the  pressure  of  wind  on  structures,  an  elaborate  series  of 
experiments  was  conducted  by  Thomas  Edward  Stanton 
and  the  results  embodied  in  two  papers  contributed  by 
him  to  the  Institution  of  Civil  Engineers:  "On  the  Ke- 
sistance  of  Plane  Surfaces  in  a  Uniform  Current  of  Air" 
and  "Experiments  on  Wind  Pressure."  For  circular 
plates  2  in.  in  diameter  at  1%  diameters  apart,  he  found 
the  value  of  the  total  pressure  was  less  than  75%  of  the 
resistance  on  a  single  plate;  at  2.15  diameters  apart  the 
total  pressure  was  equal  to  that  on  a  single  plate;  while 
at  a  distance  of  5  diameters  apart  the  total  pressure  was 
1.78  times  that  on  a  single  plate.  Stanton's  first  experi- 
ments were  criticized  because  they  were  conducted  with 
such  small  models.  For  his  second  series  he  built  a  tower 
and  used  larger  surfaces,  but  found  little  to  change  his 
previous  conclusions. 

Baker's  experiments  at  the  Forth  Bridge  led  him  to 
the  conclusion  that  in  no  case  was  the  area  affected  by  the 
wind  in  any  girder  which  had  two  or  more  surfaces  ex- 
posed more  than  1.8  times  the  area  of  the  surface  directly 
fronting  the  wind.  The  Board  of  Trade  regulations 
under  which  the  Forth  Bridge  was  built  required  that  a 
wind  pressure  of  56  Ib.  per  sq.ft.  should  be  used  in  cal- 
culations, and  this  twice  over  the  area  of  the  girder  sur- 
face exposed.* 

MEASURING  WIND  PRESSUBE  AND  VELOCITY 

It  has  been  assumed  by  experimenters  that  the  pressure 
of  the  wind  on  a  given  shape  with  a  certain  velocity  is  the 
same  as  that  of  the  shape  moving  through  the  air  with  an 
equal  velocity.  This  seems  to  follow  from  Newton's 
Corollary  V  to  his  Laws  of  Motion,  "The  motions  of  bod- 
ies included  in  a  given  space  are  the  same  among  them- 
selves, whether  that  space  is  at  rest  or  moves  uniformly 
forward  in  a  right  line  without  any  circular  motion." 

*Engineers  regard  the  requirement  of  56  Ib.  as  needless 
and  excessive. 

[  9  ] 


Perhaps  the  only  dissonant  voice  is  that  of  T.  Claxton 
Fidler,  who  in  his  Bridge  Construction  writes:  "But  it 
has  not  yet  been  ascertained  that  the  pressure  of  the  wind 
is  the  same  thing  as  the  resistance  offered  by  the  air  to 
a  moving  body." 

The  pressure  of  the  wind  has  been  measured  direct  and 
independently  of  the  velocity.  The  methods  of  doing  this 
are  so  limited  in  their  application  that  the  pressure  is 
almost  universally  determined  in  terms  of  the  velocity. 
Hence,  the  prime  importance  of  measuring  the  velocity 
of  the  wind  correctly.  Attempts  to  do  this  have  been 
made  by  all  manner  of  means  for  the  past  two  centuries. 
The  science  of  Anemometry  has  a  literature  of  its  own. 
The  velocities  obtained  by  all  methods  are  more  or  less 
in  error — some  of  them  very  much  so.  At  present  the 
Kobinson  Cup  Anemometer  or  some  modification  of  it  is 
used  pretty  generally  throughout  the  meteorological  world 
for  measuring  wind  velocities. 

In  the  Transactions  of  the  Royal  Irish  Academy,  Vol. 
XXII,  part  III  (1852),  is  a  paper:  "Description  of  an 
Improved  Anemometer  for  Registering  the  Direction  of 
the  Wind,  and  the  Space  Which  it  Traverses  in  Given  In- 
tervals of  Time.  By  the  Rev.  Tfhomas]  R[odney]  Rob- 
inson, D.D.,  Member  of  the  Royal  Irish  Academy,  and  of 
other  Scientific  Societies.  Read  June  10,  1850."  Dr. 
Robinson,  who  was  connected  with  the  observatory  at 
Armagh,  Ireland,  writes : 

After  some  preliminary  experiments  I  constructed  in  1843 
the  essential  parts  of  the  machine,  a  description  of  which 
I  now  submit  to  the  Academy,  and  I  added  in  subsequent 
years  such  improvements  as  were  indicated  by  experience. 
It  was  complete  in  1846,  when  I  described  it  to  the  British 
Association  at  Southampton. 

He  found  "from  sixteen  experiments  made  in  four  days 
with  winds  from  a  moderate  breeze  to  a  hard  gale, 

£-4.011 

or,  in  round  numbers,  the  action  on  the  concave  is  four 
times  that  on  the  convex."  From  this  he  found  the 
theoretic  value  m  of  the  ratio  of  the  velocity  of  the  wind 
to  that  of  the  cup  center  to  be  m  =  3.00.  Dr.  Robinson 
concluded  that  no  matter  what  the  size  of  the  cups  or  the 

[10] 


lengths  of  the  arms,  "the  centers  of  the  hemisphere  move 
with  one-third  of  the  wind's  velocity,  except  so  far  as  they 
are  retarded  by  friction."  This  has  been  disproved.  As 
a  necessary  result,  many  published  velocities  are  in  error. 
The  U.  S.  Weather  Bureau  prescribes  that  each  pat- 
tern of  anemometer  should  have  its  particular  law  of  ro- 
tation determined  by  special  experiment.  Its  stand- 
ard instruments  in  use  throughout  the  United  States  have 
hemispherical  cups  4  in.  in  diameter  on  arms  6.72  in. 
long  from  the  axis  to  the  center  of  the  cups.  To  the  ob- 
served velocity  the  correction  Log.  V  =  0.509  +  0.912 
Log.  v  is  applied  in  which  V  is  the  actual  velocity  of  the 
wind  and  v  is  the  linear  velocity  of  the  cup  centers,  both 
expressed  in  miles  per  hour. 

EFFECT  OF  VABIATIONS  WITHIN  THE  WIND 
Measurements  of  either  wind  velocity  or  wind  pressure 
are  complicated  enormously  by  the  variations  in  the  wind. 
This  is  illustrated  by  two  observed  facts,  both  of  which 
are  vitally  important  to  the  structural  engineer  : 

1.  Wind  pressures  are  less  per  unit  of  area  for  large 
surfaces  than  for  small  ones.     On  the  Forth  Bridge  two 
pressure  boards  were  set  up,  one  20  ft.  long  by  15  ft. 
high,  and  8  ft.  from  it  a  circular  plate  of  1%  sq.ft.  area. 
The  maximum  pressure  registered  on  the  small  plate  dur- 
ing the  years  1884  to  1890  was  41  Ib.  per  sq.ft.  The  large 
board  showed  at  the  same  time  a  pressure  of  27  Ib.  per 
sq.ft.    The  readings  for  the  large  board  never  exceeded 
80%  of  those  recorded  for  the  small  plate  at  the  same 
time,  and  generally  were  50  to  70%.    A  technical  journal 
of  the  time  hastily  drew  the  inference  from  these  experi- 
ments that  pressure  per  square  foot  varies  inversely  as 
area,  the  velocity  remaining  the   same  —  another  illus- 
tration of  generalizing  from  insufficient  data  ! 

2.  Wind  velocity  increases  with  the  distance  from  the 
ground.  Thomas  Stephenson  from  his  experiments  writes 
the  equation 


or 


[11] 


A  limiting  unit  of  height  must  be  established  for  this 
equation  to  be  of  any  use.  An  anemometer  placed  at  the 
top  of  the  Eiffel  Tower,  an  elevation  of  994  ft.,  and 
another  in  the  meteorological  office  at  an  elevation  of  69 
ft.,  showed  for  light  winds  velocities  nearly  four  times 
as  great  at  the  top  of  the  tower  as  at  the  office.  For 
higher  winds  the  velocities  came  nearer  together. 

CONCLUSION 

Cavallo,  previously  quoted,  wrote,  "a  great  many  more 
experiments  must  be  instituted  by  scientific  persons  be- 
fore the  subject  can  be  sufficiently  elucidated."  More  than 
a  hundred  years  after  Cavallo's  writing,  the  U.  S. 
Weather  Bureau  in  its  monograph  on  Anemometry, 
after  giving  values  for  pressures  and  velocities  with  all 
the  refinements  at  its  command,  says : 

Great  dependence  cannot  be  placed  in  these  values  for 
indicated  velocities  beyond  50  or  60  miles  per  hour,  as  thus 
far  direct  experiments  have  not  been  made  at  the  higher 
velocities,  though  it  is  probable  the  corrected  values  are 
throughout  much  more  accurate  than  values  computed  from 
older  formulas  and  uncorrected  wind  velocities. 

Structures  have  long  been  designed  with  satisfactory 
results  to  withstand  wind  pressure.  The  bracing  at  times 
may  have  been  excessive,  but  in  the  absence  of  better 
knowledge  on  the  subject,  engineers  cannot  radically  de- 
part from  present  practice. 


II 

Wind  Stresses  in  Steel  Mill- 
Buildings 

SYNOPSIS — Discusses  the  distribution  of  wind 
pressure  on  a  sloping  roof,  referring  to  the  experi- 
ments of  Irminger,  Kernot,  Stanton,  Smith  and 
others.  Analyses  of  stresses  in  Fink  roof  trusses 
show  that  a  uniform  vertical  excess  load  is  suffi- 
cient to  take  care  of  wind  stresses  if  rigid  mem- 
bers are  used.  In  kneebraced  mill-building  bents, 
wind  corrections  are  necessary.  Suction  effects 
are  to  be  neglected  except  as  regards  anchorage. 
Recommends  wind  pressures  and  unit  stresses,  and 
discusses  special  bracing. 

In  designing  ordinary  mill-buildings  it  is  common 
practice  either  (1)  to  neglect  the  wind  stresses  or  (2)  to 
calculate  them  in  accordance  with  some  textbook  method 
and  then  tone  down  the  results.  In  doing  the  latter,  the 
general  practice  of  designing  buildings  is  followed,  in 
conformity  to  which  structures  have  been  built  that  have 
rendered  excellent  service  for  many  years.  To  bridge  the 
gap  between  theory  and  practice,  recourse  is  being  had 
by  some  to  what  might  be  called  a  new  school,  which  has 
advanced  new  methods  and  new  experimental  results.  In 
the  present  article  this  school  will  be  briefly  reviewed,  its 
conclusions  negatived,  and  textbook  assumptions  made 
to  agree  as  near  as  possible  with  actual  conditions — the 
object  being  to  present  a  safe,  sane,  workable  method  of 
determining  and  making  provision  for  the  wind  stresses 
in  steel  mill-buildings. 

AMOUNT  AND  DISTRIBUTION  OF  WIND  STRESSES 
A  recent  writer1  of  the  new  school  states  the  case  thus : 

In  a  high  wind  the  maximum  pressure  against  the  roof 
is  at  the  windward  eaves.  The  pressure  decreases  upward 
on  the  windward  slope,  and  is  zero,  it  is  claimed,  at  a  point 


^'Insurance    Engineering,"    August,    1912. 

[  13  ] 


three-fourths  the  distance  to  the  ridge.  Beyond  the  zero 
point,  up  to  the  ridge  and  down  the  leeward  slope,  the  pres- 
sure is  negative.  The  wind  deflected  upward  by  the  wind- 
ward surface  of  the  roof  rarefies  the  air  over  the  leeward 
surface,  which  allows  the  air  inside  the  building  to  exert  an 
upward  pressure  in  excess  of  the  downward  pressure  on  the 
roof.  In  other  words,  there  is  direct  or  inward  pressure  on 
the  windward  slope  of  the  roof,  center  of  pressure  below 
middle  of  slope,  and  at  ridge  and  on  all  of  leeward  slope, 
there  is  outward  pressure  or  suction. 

SUCTION  ON  EOOF 

In  1894,  J.  0.  V.  Irminger,  manager  of  the  Copen- 
hagen Gas  Works,  made  a  number  of  experiments  on  wind 
pressure,  the  description  and  results  of  which  he  em- 
bodied in  a  paper2  to  which  reference  is  often  made.  A 
rectangular  opening  about  6%xll  in.  was  made  in  a 
chimney  5  ft.  in  diameter  and  100  ft.  high.  Into  this 
opening  was  inserted  a  conduit  4%x9  in.,  polished  on 
the  inside  to  reduce  friction.  Currents  of  air  were  made 
to  strike  plates  and  models  placed  in  this  conduit  and  the 
resultant  pressure  registered.  A  model  of  a  pitched  roof 
with  45°  slopes  showed  a  normal  uplift  on  the  leeward 
side  due  to  suction  three  times  as  great  as  the  normal 
pressure  on  the  windward  side.  The  conclusion  drawn 
was  "if  the  author's  experiments  on  models  represent  the 
facts  with  regard  to  buildings,  the  methods  with  which 
roof  principals  are  commonly  calculated  for  wind-pres- 
sure need  revision."  An  enthusiastic  admirer  of  Irminger 
writes,3  "It  will  be  due  to  him  that  we  surely  in  the 
future  shall  save  tons  of  material  in  our  roofs." 

In  1891-94,  Prof.  W.  C.  Kernot,  of  the  University  of 
Melbourne,  made  the  experiments  connected  with  his 
name.4  By  means  of  a  gas  engine  and  propeller,  he  dis- 
charged a  jet  of  air  12  in.  by  10  in.,  placing  into  this  jet 
the  plates  and  models  he  wished  to  test.  He  concluded 
that  the  usual  method  of  calculating  wind  stresses  in 
roofs  applied  only  to  roofs  supported  by  columns  under 
which  the  air  could  blow  freely.  With  roofs  of  a  low 


2"Engineering  News,"  Feb.  14,  1895;  "Engineering,"  Dec. 
7,  1895;  Proc.  Inst.  Civ.  Engrs.,  Vol.  CXVIII,  p.  468. 

•Theodore   Nielsen,    "Engineering,"    Oct.    9,    1903. 

*"Engineering  Record,"  Feb.  10,  1894;  Proc.  Inst.  Civ. 
Engrs.,  Vol.  CLXXI,  p.  218;  Australian  Association  for  the 
Advancement  of  Science,  Vol.  V  (1893),  p.  573,  Vol.  VI  (1895), 
p.  741. 

[14] 


pitch  resting  on  walls  having  parapets,  he  found  a  tend- 
ency to  an  uplift. 

In  1893  and  later,  T.  E.  Stanton,  of  the  National  Phys- 
ical Laboratory,  England,  made  the  experiments  which 
have  become  widely  known  from  the  papers  he  contrib- 
uted to  the  Institution  of  Civil  Engineers.5  From  ob- 
servations on  models  of  roofs  the  sides  of  which  were  3 
in.  by  1  in.  and  sloped  at  30°,  45°  and  60°,  placed  in  a 
current  of  air  having  velocities  of  10.0,  13.6  and  16.8 
miles  per  hour,  he  writes,  "The  experiments  appear  to 
indicate  beyond  question  the  importance  of  a  consider- 
ation of  a  negative  pressure  on  the  leeward  side  of  roofs/' 
From  later  experiments  on  pressure  boards  5x5  ft.  to 
10x10  ft.,  he  found  the  coefficients  of  wind  pressure  to  be 
as  follows : 

STANTON'S     COEFFICIENTS     k     IN     FORMULA     Pn     =     kV2 

(a)  Roof  mounted   on   columns  through  which   air   can   pass 

60°  45°  30° 

Windward   side    +0.0034          +0.0028          +0.0015 
Leeward  side  negligible 

(b)  Roofs  of  buildings  in  which  the  pressure  on  the  interior 

may   be    affected   by   the  wind. 

60°  45°                     30° 

Windward   side    +0.0034  +0.0028  +0.0015 

Leeward  side       —0.0032         — —0.0022 

This  coefficient  gives  the  normal  pressure  on  roof  sur- 
face in  Ib.  per  sq.ft.,  if  V  is  the  wind  velocity  in  miles 
per  hour,  the  wind  blowing  horizontal. 

Prof.  Albert  Smith  in  a  paper  read  before  the  West- 
ern Society  of  Engineers,  November,  1910,  entitled 
<rVVind  Loads  on  Mill  Building  Bents,"6  among  his  con- 
clusions advocates  "placing  the  wind  loads  equally  on  the 
two  walls,  and  inward  and  outward  on  the  windward  and 
leeward  roofs  respectively,  as  giving  important  changes 
of  stress  in  members  of  the  roof  truss,  as  giving  less  stress 
in  the  kneebraces  and  columns,  and  as  permitting  the 
rational  design  of  the  girts."  In  1912,  he  made  a  num- 
ber of  observations  on  a  model  building  6  ft.  wide  by 
15  ft.  long,  with  wall  heights  of  4,  5  and  6  ft.  In  a 
paper  "Wind  Pressure  on  Buildings,"7  he  writes: 

•Proc.  Inst.  Civ.  Engrs.,  Vol.  CL.VI,  p.  78,  Vol.  CLXXI,  p.  175. 
'Journal   Western   Soc.    Engrs.,    February,   1911. 
Mournal   Western    Soc.    Engrs.,    December,    1912. 

[  15  ] 


The  ordinary  methods  of  assuming  wind  loads  on  mill 
buildings  ought  to  be  somewhat  revised.  For  the  case  of  roof 
trusses  on  masonry  walls,  or  on  steel  bents  with  long  diag- 
onals, a  suction  effect  in  the  neighborhood  of  0.4  of  the  unit 
wind  pressure  should  be  placed  on  the  leeward  roof  of  all 
closed  buildings,  and  a  pressure  or  suction  derived  from  the 
curves  drawn  from  the  observations  placed  on  the  windward 
roof.  The  resulting  stresses  will  not  only  be  different  in 
amount  from  those  computed  on  the  present  basis,  but  will 
in  many  members  differ  as  to  sign.  Wind  loads  on  purlins 
might  in  most  cases  be  entirely  omitted.  *  *  *  *  In 
buildings  with  kneebraced  bents,  in  addition  to  the  preceding 
points,  the  suctions  on  the  leeward  wall  should  be  considered. 

Prof.  Boardman,  University  of  Nevada,  in  1911  made 
experiments  on  a  model  roof  10  ft.  long,  each  slope  6  ft. 
wide,  resting  on  walls  4  ft.  high.  His  conclusions  are 
similar  to  those  of  Prof.  Smith.8 

An  English  textbook,  Brightmore's  Structural  Engi- 
neering, first  issued  in  1908,  quotes  the  Stanton  experi- 
ments as  authority  and  the  stress  diagrams  for  the  roof 
truss  given  are  made  with  the  wind  forces  so  acting.  The 
heading  of  the  section  is  significant:  "Stresses  Due  to 
Wind  Pressure  and  Wind  Suction." 

Another  English  textbook,  Andrews'  The  Theory  and 
Design  of  Structures,  in  an  appendix  to  the  last  edition, 
1913,  calls  attention  to  Stanton's  conclusions  and  gives 
a  stress  diagram  for  a  truss  with  the  wind  loading  in  ac- 
cordance with  these  conclusions.  In  mentioning  the 
stresses  due  to  suction  on  the  leeward  side  the  author 
writes,  "Few  designers  appear  to  have  allowed  for  this 
in  their  calculations  for  roofs,  but  the  question  is  of  con- 
siderable importance  and  the  results  of  these  experiments 
should  either  be  disproved,  or  allowance  should  be  made 
for  them  in  design." 

Marburg  in  Framed  Structures  and  Girders  alludes  to 
the  experiments  of  Kernot,  Irminger  and  Stanton  and 
reproduces  one  of  the  Irminger  sketches.  His  practical 
conclusion  is: 

The  experiments  of  Kernot,  Irminger  and  Stanton  were 
made  on  much  too  small  a  scale  to  admit  of  quantitative  de- 
ductions applicable  to  conditions  in  practice.  They  are  val- 
uably suggestive,  however,  in  calling  attention  to  conditions 
which  were  previously  not  generally  or  adequately  recognized. 

With  this  conclusion  the  writer  is  in  thorough  accord. 


8Journal   Western    Soc.    Engrs.,    April,    1912. 

[  16  ] 


SELECTING  A  WIND  PKESSUEE  FOE  DESIGN 

Our  knowledge  of  wind  pressures  is  very  imperfect.  It 
is  generally  agreed  that  the  fundamental  equation  P  = 
kV2  is  correct  for  horizontal  wind.  There  is  little  dispute 
that  for  wind  with  a  uniform  velocity  and  normal  to 
plates  of  moderate  size,  the  value  of  k  is  from  0.0032  to 
0.004.  Of  the  formulas  for  wind  pressure  on  inclined 
surfaces  our  best  knowledge  indicates  that  of  Duchemin 
as  the  most  accurate.  It  is 

2  sin  A 
I  +  sin*  A 

There  remains  to  be  assigned  a  value  to  V.  Average 
wind  velocities  for  a  day  or  a  month  or  a  year  are  use- 
less. Shall  the  highest  wind  velocity  on  record  be  taken? 
Is  this  likely  to  occur  again? 

It  is  useless  to  attempt  to  make  provision  for  torna- 
does or  violent  hurricanes  "against  which  neither  care, 
nor  strength,  nor  wisdom,  can  avail."*  Such  storms  are 
limited  in  area  and  come  but  seldom,  perhaps  once  in  a 
century.  The  endeavor  to  make  a  mill-building  strong 
enough  to  resist  them  would  not  only  add  greatly  to  the 
cost  but  would  be  ineffective,  f 

The  highest  wind  velocity  recorded  in  New  York  City 
since  1871  by  the  U.  S.  Weather  Bureau  was  96  miles 
per  hour  sustained  for  a  period  of  five  minutes.  During 
one  minute  of  that  time  the  velocity  was  120  miles  per 
hour.  This  was  in  Feb.  22,  1912,  a  Robinson  anemom- 
eter being  used  in  the  same  location  as  at  present,  about 
20  ft.  above  the  roof  of  the  33-story  building  at  17  Bat- 
tery Place.  A  recorded  velocity  of  80  to  90  miles  is  not 
uncommon.  A  recorded  velocity  of  90  miles  per  hour 
corrected  by  the  Weather  Bureau  formula  gives  an  actual 
velocity  of  69.2  miles  per  hour.  With  this  value  in  the 
formula  P  =  kV2,  k  =  0.004,  the  normal  pressure  is 
19.2  Ib.  per  square  foot  on  a  vertical  surface.  Wind  pres- 

*This  is  the  way  it  is  stated  in  the  Foreword  of  a  little 
volume  issued  by  the  Home  Insurance  Co.,  of  New  York,  advo- 
cating windstorm  and  tornado  insurance.  More  than  a 
hundred  photographs  in  this  volume  of  wrecks  caused  by 
windstorms  illustrate  the  truth  of  the  Foreword. 

fEditor's  Note — This  argument  in  its  terms  applies  Just  as 
much  to  office  buildings  and  all  other  structures  as  it  does  to 
mill  buildings.  The  author  probably  means  to  emphasize  the 
cost  limitation,  for  mill-buildings  alone. 

[17] 


sure  increases  with  the  distance  from  the  ground  and 
decreases  per  square  foot  as  the  area  becomes  larger. 
When  it  is  remembered  that  the  instrument  above  men- 
tioned is  about  400  ft.  from  the  ground  and  the  cups 
are  only  4  in.  in  diameter,  the  assumptions  that  will  be 
made  of  a  horizontal  wind  force  of  20  Ib.  per  sq.ft.  in  de- 
signing the  trusses  of  mill-buildings,  and  15  Ib.  in  de- 
signing columns  and  kneebraces,  seem  to  be  ample  and 
fully  warranted. 

WIND  STRESSES  IN  KOOF  TRUSSES 

Eoof  trusses  resting  on  brick  walls  will  first  be  con- 
sidered. The  example  taken  will  be  a  roof  truss  as  in 
Fig.  1,  with  pitch  of  6  in.  to  1  ft.,  and  span  of  60  ft. 
c.  to  c.  of  bearing  plates.  Trusses  are  16  ft.  apart  on  cen- 
ters. For  a  horizontal  wind  from  the  left,  with  pressure 
of  20  Ib.  per  sq.ft.  on  a  vertical  surface,  the  normal  pres- 
sure on  a  surface  inclined  6  in.  to  1  ft.  will  be  (by  Du- 
chemin's  formula)  14.9  Ib.  per  sq.ft. 

The  following  cases  will  be  considered: 

(1)  Wind  load  of  15  Ib.  per  sq.ft.  or  2012  Ib.  per 
panel,  normal  to  one  slope  of  roof,  both  ends  of  truss 
fixed. 

(2)  Loads  as  in   (1),  left  end  fixed,  right  end  on 
rollers. 

(3)  Loads  as  in  (1),  left  end  rollers,  right  end  fixed. 

(4)  Load  of  15  Ib.  per  sq.ft.  exposed  surface  or  2012 
Ib.  per  panel  on  both  sides  of  the  roof,  the  loads  ap- 
plied vertically. 

The  stresses  for  these  four  cases  are  tabulated  below : 

It  is  seen  at  a  glance  that  Case  4  is  sufficient  to  cover 

wind  stresses.    The  slight  excess  in  a  few  members  found 

in  the  other  cases  is  negligible,  especially  when  they  are 

considered  with  the  combined  stresses  due  to  all  loads. 

With  the  same  wind  velocity  as  before,  according  to 
Stanton,  the  pressure  on  the  windward  slope  is  about 
n/2  Ib.  per  sq.ft.  and  22/15  times  7^  or  11  Ib.  per  square 
foot  negative  pressure  or  suction  on  the  leeward  side. 
The  forces  acting  upon  the  truss  are  as  in  Fig.  2  (reac- 
tions are  for  both  ends  fixed,  wind  shear  equally  divided), 
while  Fig.  3  is  the  stress  diagram  for  both  ends  fixed. 

[18] 


The  tabulation  of  stresses  given  below  is  for 

(5)  Both  ends  of  truss  fixed. 

(6)  Left  end  fixed,  right  end  on  rollers. 

(7)  Left  end  rollers,  right  end  fixed. 

It  might  be  stated  here  that  all  the  above  cases  with 
one  end  on  rollers  are  hypothetical,  as  roof  trusses  under 
100-ft.  span  are  seldom  built  with  other  than  fixed  ends.* 

EECOMMENDED  DESIGN  LOAD — Maximum  wind  load- 
ing comes  seldom  and  lasts  but  a  short  time.  The  work- 
ing stresses  used  for  this  loading  may  therefore  be  in- 
creased 50%  above  those  used  for  ordinary  live-  and 
dead-loads.  A  wind  load  of  15  Ib.  per  sq.ft.  is  thus  equiv- 
alent to  a  load  of  10  Ib.  using  the  working  stresses  for 
other  loads. 

The  snow  load  varies  from  20  Ib.  per  sq.ft.  horizontal 
projection  in  the  latitude  of  New  York  City  to  30  Ib.  in 
parts  of  New  England.  This  is  equivalent  to  16.6  up  to 
25  Ib.  vertical  load  per  sq.ft.  surface  of  a  6-in.  pitch 
roof. 

For  combined  snow  and  wind  a  load  of  25  Ib.  per  sq.ft. 
over  entire  surface,  acting  vertically,  is  ample  for  roofs 
in  the  latitude  of  New  York  City.  If  to  this  is  added  the 
weight  of  trusses,  purlins,  and  roof  covering,  reduced  to 
square  foot  of  exposed  surface,  we  have  the  total  load 
for  which  the  ordinary  roof  truss  should  be  designed. 
However,  not  less  than  40  Ib.  should  be  used  except  in 
tropical  climates  with  no  snow,  where  the  minimum  load- 
ing should  be  30  Ib.  Where  snows  are  severe  5  to  10  Ib. 
should  be  added  to  the  40  Ib. 

No  ALLOWANCE  FOR  SUCTION — Turning  to  the  tabu- 
lation of  stresses  found  by  the  Stanton  assumptions,  and 
taking  into  account  the  total  stresses  from  all  loads,  the 
saving  due  to  reduced  wind  stresses  is  small.  A  serious 
objection  to  taking  advantage  of  even  this  saving  is  that 
with  a  monitor  along  the  ridge,  or  openings  in  the  build- 
ing and  roof,  the  closed  roof  may  become  a  partly  open 
roof,  thus  changing  the  conditions  for  which  the  assump- 

*Editor's  Note — The  wind  shear  may,  however,  come  wholly 
on  one  or  the  other  wall,  due  to  unequal  bedding  of  the 
anchor  bolts  or  to  temperature  movement.  The  condition 
then,  as  regards  the  present  calculation,  is  identical  with  one 
end  on  rollers. 

[  19  ] 


tions  were  made.  For  a  truss  resting  on  brick  walls  the 
tendency  to  an  uplift  can  be  met  by  firmly  anchoring  it 
at  the  ends.  The  tendency  to  reversals  of  stress  can  be 
sufficiently  met  by  using  stiff  shapes  for  all  members; 
flats  and  rounds  have  no  place  in  an  ordinary  roof  truss. 
The  writer  believes  that  the  assumption  of  a  total  uni- 
form load  per  square  foot  of  exposed  surface  applied  ver- 
tically at  the  panel  points,  with  the  same  working  stresses 
used  throughout,  is  specially  well  adapted  to  the  design 
of  roof  trusses. 

WIND  STRESSES  IN  KNEEBRACED  BENTS 

KNEEBRACED  BENTS — The  case  of  an  intermediate 
transverse  bent  of  a  kneebraced  mill-building  will  now 
be  considered.  The  example  taken  will  be  that  shown  in 
Fig.  4;  span  60  ft.,  roof  pitch  6  in.  to  1  ft,  height  14  ft. 
to  foot  of  kneebrace  and  20  ft.  to  bottom  chord.  Trusses 
are  16  ft.  apart  c.  to  c. 

The  wind  pressure  will  be  taken  at  15  Ib.  per  sq.ft. 
perpendicular  to  the  sides  of  the  building  and  the  cor- 
responding normal  component  on  the  roof  at  11.2  Ib. 
(For  buildings  over  25  ft.  to  the  eave  line  the  normal 
component  of  a  wind  load  of  20  Ib.,  or  14.9  Ib.,  would 
be  used  for  the  roof.)  The  columns  are  assumed  par- 
tially fixed  at  the  lower  end,  with  the  point  of  contraflex- 
ure  at  one-third  the  distance  between  the  lower  end  and 
the  foot  of  the  kneebrace;  the  upper  ends  are  considered 
supported.  The  wind  shear  is  divided  equally  between 
the  two  columns.  Fig.  5  is  the  stress  diagram. 

Bending  moments  in  the  columns  are  as  follows : 

At  the  foot  of  windward  column 12,320  ft.-lb. 

At  foot  of  leeward  column   14,940  ft.-lb. 

At  foot  of  windward  kneebrace 19,410  ft.-lb. 

At  foot  of  leeward  kneebrace 29,870  ft.-lb. 

It  is  seen  that  the  maximum  bending  moment  is  at  the 
foot  of  the  leeward  kneebrace. 

RECOMMENDED  METHOD — For  mill-building  bents  the 
writer  first  determines  the  stresses  in  the  truss  due  to  a 
total  uniform  load  and  then  proportions  it  for  the  same. 
The  ordinary  working  values  for  medium  steel  are  gen- 

[  20  ] 


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[21] 


erally  used — 16,000  Ib.  per  sq.in.  in  net  tension  and  (re- 
duced by  formula)  for  gross  compression.  If  the  wind 
stresses  in  any  member  from  Figs.  4  and  5  are  greater 
than  the  wind  stresses  from  the  uniform  wind  loading  of 
10  Ib.  per  sq.ft.  applied  vertically,  that  member  is  pro- 
portioned for  the  maximum  wind  stress  plus  the  stresses 
from  the  uniform  loads  other  than  wind,  using  working 
stresses  50%  more  than  in  the  first  calculation;  but  in 
no  case  is  a  less  section  used  than  that  first  obtained.  The 


v^ 


FIGS.  4  AND  5.   KNEEBRACED  BENT  or  A  MILL-BUILDING  ; 
STRESS  DIAGRAM  FOR  WIND  LOAD 

(Equal   shears;   contraflexure  one-third   height  to   kneebrace) 

members  be  and  fr^  will  generally  need  be  increased; 
often  cd  and  c^;  occasionally  gd,  gf,  gf±  and  g^.  A 
reversal  of  stresses  is  noted  in  certain  members,  particu- 
larly in  ~bc  and  the  lower  chord.  The  diagonals  "be  and 
biC^  can  be  made  of  two  angles  instead  of  one  as  wher* 
designed  for  tension  alone.  The  compressive  stresses  in 
the  lower  chord  are  overcome  by  the  tensile  stresses  due 

[  22  ] 


to  the  dead-load.  The  kneebraces  have  wind  stresses  only, 
end  are  proportioned  for  the  larger  working  stresses. 

The  column  is  first  proportioned  for  carrying  the  di- 
rect stress  due  to  the  total  uniform  load  from  the  truss, 
noting  the  flange  area  required.  From  the  maximum 
bending  moment  due  to  the  wind,  as  in  Fig.  4  and  5,  the 
sectional  area  required  for  the  flanges  is  found  using  the 
larger  working  stresses  and  considering  the  column  as 
a  beam.  If  this  flange  area  is  not  more  than  one-third 
of  that  first  found  no  change  is  made;  if  more  than  one- 
third,  the  excess  is  added.  The  compressive  stress  due 
to  overturning  need  not  be  considered  unless  it  exceeds  the 
stress  from  the  wind  portion  of  the  uniform  roof  load. 

GIKTS — The  side  and  end  girts  are  proportioned  as 
beams  supported  at  each  end  with  a  uniform  horizontal 
load  of  15  Ib.  per  sq.ft.;  an  extreme  fiber  stress  of  24,000 
Ib.  per  sq.in.  is  used. 

The  girts  are  apparently  the  simplest  portion  of  the 
building  to  design,  but  if  observation  and  experience 
count  they  are  the  most  difficult.  Side  and  end  girts  of 
3%x2%x}4-iii.  or  ^-in.  angles,  16  to  20  ft.  long  and 
5  ft.  apart,  are  still  in  use  after  20  years'  service,  in  de- 
fiance of  all  figures.  Notwithstanding  this,  such  design- 
ing practice  is  reprehensible. 

SPECIAL  CASES  OF  MILL-BUILDING  BRACING 

Traveling  cranes  running  through  a  building  often  bar 
the  use  of  kneebraces.  The  gussets  connecting  the  trusses 
to  the  columns  should  then  be  as  large  as  possible  and 
calculations  made  accordingly.  An  ideal  way  is  to  trans- 
fer the  transverse  thrust  from  the  wind  as  well  as  that 
from  the  cranes  to  the  ends  of  the  building  by  means  of 
diagonal  bracing  in  the  plane  of  the  lower  chords  of  the 
trusses,  and  thence  by  diagonals  in  the  ends  of  the  build- 
ing to  the  ground.  Openings  in  the  ends  often  interfere 
with  this  expedient.  Neither  is  it  feasible  in  buildings 
so  long  as  to  require  provision  for  longitudinal  expan- 
sion and  contraction  due  to  changes  in  temperature. 

In  all  cases  diagonal  bracing  should  be  introduced  into 
the  planes  of  both  top  and  bottom  chords  for  stiffness  as 
well  as  to  take  calculated  stresses.  This  applies  also  to 

[  23  ] 


roof  trusses  resting  on  brick  walls.  Adjustable  rods  can 
be  used  for  top-chord  bracing,  but  the  bracing  of  the 
bottom  chord  should  be  entirely  of  angles  or  other  rigid 
shapes,  with  bolted  or  riveted  connections. 

The  ends  of  a  building,  the  gables  in  particular,  are 
more  liable  to  be  severely  strained  from  wind  than  any 
other  portion  of  the  building.  Generally  diagonals  in 
the  planes  of  the  chords  of  each  end  panel,  and  in  each 
end  side  bay  to  the  ground  will  be  sufficient  to  take  care 
of  the  induced  stresses.  If  not,  the  shear  may  be  divided 
with  other  braced  bays. 

Special  types  of  buildings  should  be  considered  in  ref- 
erence to  their  own  requirements.  Open  sheds,  especially 
if  the  gables  are  closed,  may  have  an  uplift  as  well  as  a 
vertical  load. 

COMMENTS  ON  PRIOR  KECOMMENDATIONS 

The  leading  textbook  on  the  subject  of  mill  building!, 
is  Ketchum's  Steel  Mill-Buildings.  In  this  book  a  knee- 
braced  mill  bent  is  considered  for  four  cases: 

(1)  A  horizontal  wind  load  of  20  Ib.  per  sq.ft.  on  the 
side  and  vertical  projection  of  the  roof,  with  the  columns 
Mnged  at  the  base. 

(2)  Same  wind  load  as  in  Case  1,  with  columns  fixed 
at  the  base. 

(3)  A  horizontal  wind  load  of  20  Ib.  per  sq.ft.  on  the 
side,  and  the  normal  component  of  a  horizontal  wind  load! 
cf  30  Ib.  per  sq.ft.  on  the  roof,  with  columns  hinged  at 
the  base. 

(4)  Same  wind  load  as  in  Case  3,  with  columns  fixed 
at  the  base. 

The  writer  believes  that  the  loads  of  20  and  30  Ib.  are 
larger  than  need  be  used.  The  columns  are  seldom  if 
ever  rigidly  fixed  at  the  base,  neither  are  they  hinged. 
That  they  are  partially  fixed  and  the  point  of  contra- 
iiexure  is  at  one-third  the  distance  from  base  to  foot  of 
kneebrace  is  believed  to  be  nearer  correct  than  either  as- 
suming it  one-half  the  distance  or  assuming  the  columns 
supported  at  the  base.  There  seems  no  good  reason  for 
assuming  a  normal  component  of  a  horizontal  wind  load 
of  30  Ib.  on  the  roof  while  a  horizontal  wind  load  of  20 

t  24] 


Ib.  is  taken  on  the  sides.  It  is  not  clear  why  the  Hut- 
ton  formula  is  used  to  find  the  normal  component.  Near 
the  beginning  of  the  book  we  read,  "Button's  formula  is 
based  on  experiments  which  were  very  crude  and  probably 
erroneous.  Duchemin's  formula  is  based  on  very  care- 
ful experiments  and  is  now  considered  the  most  reliable 
formula  in  use."  The  specifications  near  the  close  of  the 
book  call  for  the  Duchemin  formula  to  be  used  in  com- 
puting the  normal  wind  pressure;  by  this  formula,  for  a 
30-lb.  load,  the  18-lb.  normal  pressure  in  Cases  3  and 
4  would  be  22 A  Ib.  The  only  increase  of  the  usual  work- 
ing stresses  allowed  is  25%  for  laterals  and  50%  for 
combined  direct  and  flexural  stress  due  to  wind.  This  in- 
crease does  not  apply  to  the  combination  of  wind  with 
other  loads  though  with  the  maximum  wind  load  a  min- 
imum snow  load  of  10  Ib.  per  sq.ft.  is  allowed.  (For 
the  purpose  of  aiding  those  who  wish  to  make  compari- 
sons the  same  roof  truss  and  bent  have  been  taken  in 
this  article  as  found  in  Ketchum.) 

The  chapter  on  "Iron  and  Steel  Mill-Building  Con- 
struction" by  G.  H.  Hutchinson  in  Johnson,  Bryan  & 
Turneaure's  Modern  Framed  Structures,  considers  three 
cases  of  a  mill-building  bent,  arriving  at  conclusions  sim- 
ilar to  those  of  Ketchum.  The  method  of  obtaining  re- 
actions and  moments  is  quite  abstruse  and  difficult  to 
follow.  No  mention  is  made  in  the  chapter  of  working 
stresses  to  be  used. 

Smith,  in  "Wind  Loads  on  Mill-Building  Bents,"6  as- 
sumes a  total  horizontal  wind  force  of  30  Ib.  per  sq.ft. 
on  the  bent  considered  in  this  article.  The  pressure  on 
the  sides  is  divided  equally  between  the  two  columns. 
One-third  of  the  normal  component  of  the  total  pressure 
on  the  roof,  found  by  Duchemin's  formula,  is  taken  by 
the  windward  slope  and  two-thirds  as  suction  or  an  out- 
ward pressure  on  the  leeward  slope.  The  bases  of  the 
columns  are  considered  hinged.  Comparing  his  results 
with  those  obtained  by  Ketchum,  he  shows  reduced 
stresses  but  is  unfortunate  in  the  example  selected  for 
comparison:  Ketchum's  stresses  are  taken  and  50%  is 
added  to  them  for  a  30-lb.  load;  but  Ketchum  calculate? 
his  roof  for  the  normal  component  of  a  horizontal  wind 

[  25  ] 


of  30  Ib.  and  the  side  for  20  lb.,  so  that  Smith  is  actually 
comparing  his  results  with  those  obtained  from  a  bent 
having  a  pressure  on  the  sides  of  30  lb.  per  sq.ft.  and 
on  the  roof  the  normal  component  (by  the  Hutton  for- 
mula) of  a  horizontal  force  of  45  lb.  per  sq.ft. 

However,  with  the  same  wind  force,  the  Smith  method 
does  give  reduced  stresses,  especially  in  the  columns, 
kneebraces  and  girts.  The  important  point  is  whether 
these  reductions  are  permissible.  In  a  modern  mill-build- 
ing the  sides  are  from  one-fourth  to  one-half  or  more  of 
glass,  a  large  proportion  of  which  can  be  opened  to  permit 
of  ventilation.  If  opened  on  one  side  only,  Smith's  as- 
sumption that  the  pressure  on  the  inside  of  a  mill-build- 
ing is  a  mean  between  the  windward  pressure  and  the  lee- 
ward suction  disappears.  In  a  high  wind  the  windows  on 
the  leeward  side  are  liable  to  be  open  and  those  on  the 
windward  side  closed;  there  is  then  little  suction.  In  a 
building  the  sides  of  which  are  covered  with  sheet  metal 
there  is  always  a  probability  of  the  covering  on  one  side  or 
end  being  removed  for  8  ft.  or  more  from  the  ground, 
thus  completely  doing  away  with  the  suction  theory.  For 
these  reasons  it  is  unwise  to  take  advantage  of  a  theory 
based  upon  assumptions  which  are  destroyed  by  a  prob- 
able change  of  conditions. 

In  conclusion,  while  the  methods  advocated  for  treat- 
ing wind  stresses  may  not  be  thoroughly  scientific,  they 
are  easily  workable,  and  experience  proves  that  they  art 
safe  and  sane.  The  load  of  15  lb.,  the  working  stress  of 
24,000  lb.,  and  the  assumed  point  of  contraflexure,  may 
all  be  criticized,  but  for  the  ordinary  mill-building  it  is 
more  rational  to  use  these  assumptions  and  make  strict 
provision  for  them  than  to  follow  the  present  method  of 
giving  an  intellectual  assent  to  the  theories  of  the  text- 
book and  ignoring  them  in  actual  practice. 


Ill 

Wind  Stresses  in  Railroad 
Bridges 

SYNOPSIS— The  Tay  Bridge  failure  reviewed. 
English  practice  in  the  70's  ignored  wind  stresses, 
while  American  engineers  used  methods  nearly 
equal  to  those  of  today.  Empirical  development 
is  the  basis  of  practice.  Modern  specifications 
show  a  great  number  of  variations  in  detail,  but 
may  be  brought  nearer  uniformity  in  the  future. 
Lateral-oscillation  forces  should  be  specified  sepa- 
rate from  wind  pressure. 

The  purpose  of  this  article  is  to  review  past  and  pres- 
ent practice  of  the  treatment  of  the  wind  forces  acting  on 
railroad  bridges. 

THE  TAY  BKIDGE 

On  the  evening  of  Dec.  28,  1879,  occurred  the  "Tay 
Bridge  Disaster."  During  a  violent  gale,  11  spans  of 
245  ft.  and  two  of  227  ft.,  with  the  train  passing  over 
them  at  the  time,  fell  into  the  river.  This  failure  of  what 
was  at  the  time  the  largest  bridge  in  the  world  after  a 
service  of  less  than  two  years  marked  an  epoch  in  bridge 
building  in  Great  Britain.  "Wind  stresses  in  railroad 
bridges  had  previously  been  almost  neglected;  from  that 
time  they  have  been  fully  considered,  if  not  magnified.  A 
Court  of  Inquiry  was  appointed  by  the  English  Board  of 
Trade  to  report  on  the  causes  of  the  disaster.  Today  the 
testimony  taken  regarding  the  provision  made  in  the  de- 
sign of  the  bridge  for  wind  stresses  is  interesting  reading. 

Sir  George  Airy,  Astronomer  Eoyal,  testified  that  about 
seven  years  previously  he  had  been  consulted  on  the  sub- 
ject of  the  provision  which  should  be  made  for  wind  pres- 
sure on  the  plans  prepared  by  Sir  Thomas  Bouch  of  a 
bridge  of  two  spans  of  1600  ft.  over  the  Forth.  He  gave 
as  his  opinion  that  the  greatest  wind  pressure  that  might 
be  expected  over  the  whole  extent  of  such  a  surface  was 
10  Ib.  per  sq.ft. 

[27] 


Sir  Thomas  Bouch,  the  designer  of  the  Tay  bridge,  tes- 
tified that  he  did  not  specially  make  any  allowance  for 
wind  pressure,  but  he  had  seen  the  report  on  the  Forth 
Bridge;  he  thought  the  greatest  pressure  would  be  about 
10  Ib. 

The  majority  report  of  the  Court  of  Inquiry  ends : 

In  conclusion,  we  have  to  state  that  there  is  no  require- 
ment issued  by  the  Board  of  Trade  respecting  wind  pressure, 
and  there  does  not  appear  to  be  any  understood  rule  in  the 
engineering  profession  regarding  wind  pressure  in  railway 
structures;  and  we  therefore  recommend  that  the  Board  of 
Trade  should  take  such  steps  as  may  be  necessary  for  the 
establishment  of  rules  for  that  purpose. 

A  minority  report  was  submitted  by  the  third  member 
of  the  Court. f  An  extract  is: 

It  is  said  that  Sir  Thomas  Bouch  must  be  judged  by  the 
state  of  our  knowledge  of  wind  pressure  when  he  designed 
and  built  the  bridge.  Be  it  so;  yet  he  knew  or  might  have 
known  that  at  that  time  the  engineers  in  France  made  an 
allowance  of  55  Ib.  per  sq.ft.  for  wind  pressure,  and  in  the 
United  States  an  allowance  of  50  Ib. 

In  the  engineering  literature  of  1880  and  1881,  a 
paper  often  referred  to  is  "The  Tay  Bridge,"  by  Edgar 
Gilkes,  a  member  of  the  firm  building  the  bridge.  It 
was  read  before  the  Cleveland  Institution  of  Engineers, 
Nov.  6,  1876.  The  special  paragraph  that  must  have 
plagued  the  author  reads: 

A  consideration  of  the  action  of  the  wind  on  this  bridge 
will  dissipate  the  often-advanced  theory  that  at  some  period 
it  will  be  blown  over.  The  exposed  surface  of  one  large  pier 
is  about  800  sq.ft.,  and  of  the  superstructure  which  depends 
upon  it,  about  800  more,  and  so,  giving  800  ft.  for  a  train 


tThe  majority  of  the  Court  of  Inquiry  reported  that  in 
their  opinion  the  cross  bracing  at  the  pier  and  its  fastening 
by  lugs  was  the  first  part  to  yield.  The  evidence,  however, 
was  ample  to  justify  the  language  of  the  minority  report, 
"that  this  bridge  was  badly  designed,  badly  constructed,  and 
badly  maintained,  and  that  its  downfall  was  due  to  inherent 
defects  in  the  structure  which  must  sooner  or  later  have 
brought  it  down." 

The  piers  which  failed  carried  two  adjoining  trusses  and 
consisted  of  a  hexagonal  group  of  six  cast-iron  columns 
filled  with  Portland  cement,  two  18  in.  and  four  15  in.  in 
diameter.  Each  column  in  case  of  the  higher  columns  was 
made  of  seven  lengths  10  ft.  10  in.  long,  united  by  flanges. 
These  columns  were  braced  vertically  on  the  exterior  sides 
by  struts  of  two  6-in.  channels  and  diagonals  of  4%x%-in. 
flats  fastened  to  cast-iron  lugs  with  1%-in.  bolts.  Horizontal 
bracing  connected  the  four  interior  columns.  It  will  readily 
be  seen  that  such  a  system  is  weak  throughout. 

As  a  matter  of  interest  it  may  be  noted  that  during  the 
progress  of  construction  on  the  night  of  Feb.  2,  1877,  two  of 
the  245-ft.  spans  were  blown  into  the  river.  To  this  accident 
"Engineering"  of  Feb.  9,  1877,  devoted  just  14  lines. 


above,  we  have  2400  ft.  Twenty-one  pounds  per  sq.ft.  is 
the  force  of  a  very  strong  gale,  but  it  would  take  no  less 
than  96  Ib.  per  sq.ft.  on  the  surface  given  to  overturn  the  pier. 
Even  the  most  severe  hurricane  on  record  would  equal  only 
one-half  this  resultant  power. 

C.  Shaler  Smith,  after  a  careful  calculation  in  accord- 
ance with  American  rules,  found  the  exposed  surface  of 
the  superstructure  to  be  2576  sq.ft.  instead  of  800,  while 
the  London  Engineering  shows  the  exposed  train  surface 
was  1630  sq.ft.  instead  of  800. 

EAKLY  ENGLISH  PRACTICE 

It  is  surprising  how  little  is  found  in  the  English 
technical  books  and  papers  of  those  days  regarding  the 
force  of  the  wind  on  structures.  Humber,  in  his  volum- 
inous "Complete  Treatise  on  Cast-  and  Wrought-Iron 
Bridge  Construction,"  published  in  1861,  does  not  mention 
it.  TJnwin's  "Wrought-Iron  Bridges  and  Roofs,"  1869, 
was  a  far  better  textbook  than  any  that  had  preceded  it. 
What  he  writes  regarding  wind  pressure  on  roofs  is  still 
quoted;  yet  he  says  nothing  of  wind  stresses  in  bridges. 
The  article  on  Bridges,  by  Prof.  Jenkin,  in  the  ninth 
edition  of  the  "Encyclopedia  Britannica"  (1876),  after- 
ward issued  as  a  separate  treatise,  fills  58  closely  written 
pages,  but  not  a  line  is  found  concerning  wind  bracing. 
Thomas  Cargill,  in  his  "The  Strains  upon  Bridge  Gird- 
ers and  Eoof  Trusses,"  1873,  writes : 

No  allowance  is  made  in  the  theoretical  calculation  for  the 
violent  shock,  concussion  and  consequent  vibration  that  attend 
the  passage  of  a  heavy  train  over  a  bridge.  This  must  be 
allowed  for  by  experience,  by  the  introduction  of  such  addi- 
tional bracing  as  the  skill  of  the  engineer  suggests.  These 
are  points  which  cannot  be  learned  from  books. 

To  the  effect  of  the  wind  on  a  bridge  he  makes  no  al- 
lusion, though  in  the  chapter  "Curved  Roof  Trusses,"  he 
says: 

Some  writers  lay  great  stress  upon  providing  a  large 
margin  of  strength  for  wind  pressure,  but  there  is  more 
theoretical  than  practical  knowledge  displayed  in  such  state- 
ments. 

Rankine,  in  his  "Manual  of  Civil  Engineering,"  in  the 
early  60's,  gives  a  formula  for  the  effect  of  wind  on  tubular 
girders,  and  in  a  footnote  states  that  the  greatest  pres- 
sure of  wind  ever  observed  in  Britain  was  55  Ib.  per  sq.ft., 

[29] 


but  we  have  no  record  that  this  observation  ever  entered 
into  the  consideration  of  bridge  engineers. 

The  first  German  edition  of  Hitter's  "Elementary  The- 
ory and  Calculation  of  Iron  Bridges  and  Roofs,"  was  is- 
sued in  1862.  An  English  translation  was  published  in 
1879.  In  this  book  the  lateral  force  is  taken  as  a  per- 
centage of  the  combined  vertical  live-  and  dead-loads.  In 
one  particular  bridge  under  consideration,  it  is  assumed 
to  be  one-seventh. 

The  outcome  of  the  agitation  following  the  fall  of  the 
Tay  Bridge  was  a  commission  appointed  by  the  Board 
of  Trade  to  consider  the  question  of  wind  pressure  on  rail- 
way structures.  This  committee  made  its  report  in  1881. 
The  substance  of  its  five  recommendations  was:  (1) 
That  for  railway  bridges  and  viaducts  a  maximum  wind 
pressure  of  56  Ib.  per  sq.ft.  should  be  assumed  for  the 
purpose  of  calculation.  (2)  That  the  area  of  exposed  sur- 
face should  be  taken  at  once  to  twice  the  front  surface, 
according  to  the  extent  of  the  openings  in  the  trusses  or 
lattice-girders.  (3)  That  a  factor  of  safety  of  4  should 
be  used  for  strains  caused  by  wind  pressure,  and  for  the 
whole  structure  overturning  as  a  mass  a  factor  of  safety 
of  2  should  be  used.  These  recommendations  became  law 
in  Great  Britain. 

EARLY  AMERICAN  PRACTICE 

Not  less  interesting  is  the  historical  development  of 
wind  bracing  in  the  United  States.  In  1851  was  pub- 
lished, "General  Theory  of  Bridge  Construction,"  by 
Herman  Haupt,  A.M.,  General  Superintendent  of  the 
Pennsylvania  R.R.,  formerly  professor  of  Mathematics 
in  Pennsylvania  College.  The  pioneer  book  in  which 
bridge  trusses  are  correctly  analyzed  is  "A  Work  on 
Bridge  Building,"  by  Squire  Whipple,  published  at  Utica, 
N.  Y.,  in  1847.  Whipple's  book  was  little  known  for  a 
ong  time  after  its  publication,  while  Haupt's  book,  written 
without  any  knowledge  of  the  existence  of  Whipple's,  soon 
became  widely  circulated  and  for  years  was  regarded  as 
an  authority.  In  Part  1  of  Haupt's  book  we  read : 

The  use  of  lateral  bracing  is  principally  to  guard  against 
the  effects  of  wind,  and  other  disturbing  causes,  tending  to 
produce  lateral  nexure  in  the  roadway  *  *  *  The  greatest 

[30] 


lateral  strain  is  that  produced  by  the  action  of  a  high  wind; 
assuming  the  force  of  wind  at  15  Ib.  per  sq.ft.,  as  a 
maximum,  *  *  * 

In  Part  II,  written  some  time  after  Part  I,  we  read, 
"The  heaviest  locomotives  in  use  weigh  about  23  tons, 
and  their  length  is  23  ft.,"  and  further  on : 

The  greatest  strain  upon  the  lateral  bracing  of  a  bridge 
would  be  that  caused  by  the  action  of  the  wind  in  a  violent 
tornado.  It  is  probable  that  this  force  is  far  greater  than 
it  is  usually  estimated.  The  observations  of  the  writer  at 
the  Susquehanna  Bridge,  during  the  tornado  which  caused 
the  loss  of  six  of  the  unfinished  spans,  led  him  to  believe  that 
the  direct  effect  of  the  storm  was  increased  by  reflection  from 
the  surface  of  the  water.  *  *  *  If  we  suppose  a  storm 
could  be  so  violent  as  to  cause  a  pressure  of  30  Ib.  per 
sq.ft.,  *  *  * 

The  tornado  alluded  to  occurred  Mar.  27,  1849.  A 
viaduct  across  the  Susquehanna  River,  near  Harrisburg, 
was  being  built  for  the  Pennsylvania  R.R.  It  was  sup- 
ported on  22  piers,  160  ft.  center  to  center.  The  trusses 
were  of  the  Howe  type,  with  the  addition  of  wooden 
arches.  After  the  fourteenth  span  had  been  raised,  the 
storm  came  and  carried  off  six  spans.  The  contractor  was 
busy  at  the  time  putting  in  the  arches,  and  as  the  diagonal 
braces  could  not  be  fastened  until  after  the  arches  were 
in  place,  they  had  been  omitted  except  over  the  piers  and 
in  the  middle  of  the  spans.  The  wind  came  at  right  angles 
to  the  bridge  and  the  six  spans  without  lateral  bracing 
gave  way. 

As  late  as  the  early  70's  American  textbooks  had  little 
or  nothing  to  say  on  wind  bracing.  De  Yolson  Wood  de- 
votes less  than  one-half  a  page  to  the  subject  in  his 
"Theory  on  the  Construction  of  Bridges,"  while  Greene 
in  "Bridge  Trusses"  spares  only  a  page.  Col.  Merrill,  in 
his  "Iron-Truss  Bridges  for  Railroads,"  makes  no  men- 
tion of  wind  bracing.  Shreve,  whose  "Treatise  on  the 
Strength  of  Bridges  and  Roofs"  was  translated  into 
French,  finds  vertical  strains,  horizontal  strains,  chord 
strains,  brace  strains,  but  the  word  wind  does  not  occur  in 
the  book,  nor  is  any  mention  made  of  bracing  in  a  hori- 
zontal plane.  Nearly  the  same  might  be  written  of  Roeb- 
ling's  "Long  and  Short  Span  Railway  Bridges/'  1869. 

American  practice,  however,  was  ahead  of  the  teaching 
profession.  C.  Shaler  Smith,  on  Dec.  15,  1880,  presented 

[31  ] 


a  masterly  paper  to  the  American  Society  of  Civil  Engi- 
neers, entitled,  "Wind  Pressure  upon  Bridges."  He 
gives  specifications  which  he  had  used  in  constructing  a 
number  of  bridges,  some  of  them  high  and  in  exposed  lo- 
calities. He  specifies : 

The  portal,  vertical  and  horizontal  bracing  shall  be  pro- 
portioned for  a  wind  pressure  of  30  Ib.  per  sq.ft.  on  the 
surface  of  a  train  averaging-  10  sq.ft.  per  lin.ft.,  and  on 
twice  the  vertical  surface  of  one  truss.  The  300  Ib.  pressure 
per  lin.ft.  due  to  the  train  surface  shall  be  treated  as  a  mov- 
ing load,  and  the  pressure  on  the  trusses  as  a  fixed  load. 
Trusses  of  less  than  200  ft.  span  shall  also  be  proportioned 
for  a  pressure  of  50  Ib.  per  sq.ft.  where  unloaded,  and  the 
greatest  strain  by  either  method  of  computation  shall  in 
each  case  be  used  in  determining  the  sectional  area  of  the 
bracing. 

Several  leading  railway  companies  at  that  time  were  us- 
ing practically  these  specifications.  From  this  same  paper 
the  following  is  significant : 

Many  engineers  prefer  to  express  wind  force  in  pounds 
per  lineal  foot  of  bridge  instead  of  per  square  foot  of  exposed 
surface.  Using  a  200-ft.  span  as  an  example,  the  specifications 
in  question  can  be  condensed  as  follows: 

Fixed    load    in    plane    of    roadway,    210    Ib.    per    lin.ft. 

Fixed   load   in   plane   of   other   chord,   130   Ib.   per   lin.ft. 

Moving    load    in    plane    of    roadway,    300    Ib.    per    lin.ft. 

It  is  refreshing  to  see  C.  Shaler  Smith  quoted  as  the 
exponent  of  American  practice  for  wind  bracing  in  the 
article  on  Bridges,  by  Unwin,  in  the  eleventh  edition  of 
the  "Encyclopedia  Britannica." 

The  rules  in  the  Erie  Specifications,  formulated  in 
1878  by  Theodore  Cooper,  were: 

To  provide  for  wind  strains  and  vibrations,  the  top  lateral 
bracing  in  deck  bridges  and  the  bottom  lateral  bracing  in 
through  bridges  shall  be  proportioned  to  resist  a  lateral  force 
of  450  Ib.  for  each  foot  of  the  span,  300  Ib.  of  this  to  be 
treated  as  a  moving  load. 

The  bottom  lateral  bracing  in  deck  bridges  and  the  top 
lateral  bracing  in  through  bridges  shall  be  proportioned  to 
resist  a  lateral  force  of  150  Ib.  for  each  foot  of  the  span. 

It  is  thus  seen  that  in  the  early  days  of  iron  railway 
bridges,  the  American  engineers  were  far  in  advance  of 
their  English  brethren  in  the  recognition  of  wind  forces. 

FACTORS  IN  THE  PROBLEM 

"A  Practical  Treatise  on  Bridge  Construction/'  by  T. 
Claxton  Fidler,  was  published  in  London  in  1887.  Chap- 

[  32  ] 


ter  XXIV  is  "On  Wind-Pressure  and  Wind-Bracing."  In 
1894,  Captain  (now  General)  Bixby,  U.  S.  A.,  in  a  mono- 
graph reviewing  the  literature  on  wind  pressure,  writes: 
"The  chapter  is  perhaps  the  best  single,  short,  concise, 
comprehensive  and  practical  review  of  the  whole  sub- 
ject yet  in  print."  This  characterization  in  a  large 
measure  still  holds  true.  Some  concluding  sentences  from 
the  chapter  are: 

We  have  seen,  for  example,  how  large  a  proportion  of  the 
metal  in  a  long-span  bridge  is  required  for  the  purpose  of 
resisting  wind-pressure  and  for  the  purpose  of  carrying  the 
metal  that  resists  wind-pressure.  But  we  have  also  seen 
that  it  is  really  impossible  to  estimate  the  wind  stresses 
within  100%  of  their  real  value.  *  *  *  In  this  state  of  un- 
certainty, the  responsible  engineer  will  generally  be  disposed 
to  err  on  the  safe  side;  but  it  must  be  remarked  that  this 
will  be  a  very  expensive  proceeding.  *  *  *  On  the  other 
hand,  he  knows  that  an  error  in  the  opposite  direction  might 
be  attended  with  still  more  disastrous  results. 

The  sting  of  these  sentences  is  in  their  truth.  Our 
knowledge  of  the  wind  is  uncertain,  especially  regarding 
the  higher  velocities.  Although  there  are  many  unknown 
quantities  in  the  problem  of  wind  stresses  in  a  bridge, 
the  main  questions  to  be  considered  are  two : 

(1)  What  is  the  pressure  to  be  assumed  per  unit  of 
area? 

(2)  What  shall  be  taken  as  the  area  exposed  to  the  ac- 
tion of  the  wind? 

Wind  pressure  is  generally  measured  in  terms  of  the  ve- 
locity. According  to  the  best  information  we  have,  an  in- 
dicated velocity  by  the  ( Weather-Bureau  standard)  ane- 
mometer of  100  miles  per  hour  denotes  an  actual  velocity 
of  76  miles,  which  is  equivalent  to  a  pressure  of  23  Ib. 
per  sq.ft.  on  a  surface  at  right  angles  to  its  direction.  A 
pressure  of  30  Ib.  per  sq.ft.,  which  corresponds  to  an 
indicated  velocity  of  about  120  miles  per  hour,  will  over- 
turn empty  freight  cars,  the  ordinary  passenger  car, 
and  acting  over  an  extended  area  of  land  would  sweep 
from  it  all  trees.  No  engine  driver  could  take  his  train 
upon  a  bridge  with  such  a  pressure,  though  it  is  possible 
that  the  train  during  a  sudden  gust  might  be  caught  there. 
A  man  could  not  keep  his  feet  with  such  a  pressure,  no 
matter  at  what  angle  his  legs  were  inclined  to  the  ground. 

[33] 


It  would  seem  that  30  Ib.  per  sq.ft.  is  ample  for  assumed 
wind  pressure. 

The  second  question  to  be  considered  is  even  more  diffi- 
cult to  answer  than  the  first.  In  a  bridge  composed  of  two 
or  more  trusses  several  feet  apart,  and  each  truss  made 
up  of  members  which  may  shelter  other  members,  the  case 
is  far  different  from  that  of  wind  on  a  plate  or  on  a  solid 
body.  Our  actual  knowledge  of  the  subject  is  slight. 
Baker's  experiments  at  the  Forth  Bridge*  and  Stanton's 
experiments  at  the  National  Physical  Laboratory f  are 
generally  quoted.  Bridge  engineers  and  writers  on  the 
subject  vary  in  their  methods.  C.  Shaler  Smith,  as  pre- 
viously noted,  uses  an  exposed  area  of  "twice  the  vertical 
surface  of  one  truss."  In  estimating  the  vertical  surface 
of  one  truss  he  adds  to  the  elevation  of  the  upper  chord 
and  posts,  as  seen  on  the  drawing,  1%  times  the  surface  of 
the  ties,  and  twice  the  surface  of  the  lower  chord.  J  Du 
Bois,  in  his  "The  Stresses  in  Framed  Structures,"  gives 
as  a  rule  this  method  for  finding  the  area  of  surface  of  a 
single  truss.  "In  preliminary  estimates,"  he  writes, 
"we  may  take  the  exposed  surface  for  both  trusses  at  10 
sq.ft.  per  lin.ft." 

Johnson,  Bryan  and  Turneaure,  in  "The  Theory  and 
Practice  of  Modern  Framed  Structures,"  use  "the  ex- 
posed surface  of  all  trusses  and  the  floor  as  seen  in  ele- 
vation." Merriman  and  Jacoby,  in  "A  Text  Book  on 
Eoofs  and  Bridges,"  Heller  in  "Stresses  in  Structures," 
and  a  number  of  other  writers  do  the  same.  "Structural 
Engineering,"  an  English  textbook  by  Husband  and 
Harby,  says  "The  area  of  the  bridge  exposed  to  the  higher 
pressure  will  be  from  once  to  about  three  times  the  area 
as  seen  in  elevation,  depending  on  the  type  of  construc- 
tion." Another  English  textbook,  Anglin,  "The  Design 
of  Structures,"  says,  "In  double-webbed  lattice  girders,  the 
area  of  both  webs  should  be  taken,  or  double  the  web  area 
as  seen  in  elevation,  .  .  .  .  If  a  bridge  consists  of 
two  such  main  girders,  the  wind  pressure  must  be  taken 
as  acting  on  an  area  equal  to  four  times  that  as  seen  in 

*  "Engineering-,"  Sept.  5,  1884. 

f'Proc.  of  Inst.  of  C.  E.,"  Vol.  CLVI  and  Vol.  CLXXI. 
t"Trans.  Am.   Soc.   C.   E.,"  Vol  X,  pp.   170.      (Private  letter 
to  O.   Chanute.) 

[  34] 


elevation."  This  same  textbook  adds,  "American  engi- 
neers assume  a  wind  pressure  of  30  Ib.  per  sq.ft.  upon 
the  loaded,  and  50  Ib.  upon  the  unloaded  structure." 

From  the  foregoing  it  is  readily  seen  that  specifications 
that  simply  give  the  load  per  square  foot  of  exposed  sur- 
face to  be  used  do  not  fully  specify.  Descriptions  of 
bridges  which  state  the  lateral  pressure  per  square  foot 
used  in  the  calculations  without  defining  the  extent  of  ex- 
posed surface  intended  by  the  designer  are  incomplete 
in  their  description. 

It  is  to  be  remembered  that  there  are  stresses  due  to  lat- 
eral forces  other  than  the  wind.  A  considerable  lateral 
force  is  developed  by  a  rapidly  moving  train,  or  the  lurch- 
ing of  a  locomotive  when  it  first  strikes  a  bridge.  This 
lateral  vibration  appears  to  be  much  more  accidental  in 
its  character  than  the  vertical  vibration.*  Even  were  there 
no  wind,  rigidity  would  have  to  be  maintained  against 
this  lateral  vibration,  which  in  short  spans  is  probably  a 
greater  factor  than  the  wind  pressure  itself.  We  have 
nothing  to  determine  a  relation  between  lateral  vibration 
and  wind  strain. 

Further,  the  compression  chords  of  bridges  must  be  held 
in  alignment  by  the  lateral  bracing.  The  amount  of  ma- 
terial required  to  do  this  is  not,  with  our  present  knowl- 
edge, a  matter  of  exact  calculation.! 

In  some  specifications  provision  for  all  lateral  forces, 
except  the  centrifugal  force  when  the  track  is  on  a  curve, 
is  included  in  that  for  wind  pressure  without  being  so 
stated.  In  others,  "for  lateral  forces"  or  "for  wind  loads 
and  lateral  vibration"  are  the  words  used  and  more  clearly 
express  what  is  intended. 

Giving  the  lateral  force  in  terms  of  pounds  per  lineal 
foot  of  bridge  (rather  than  in  pounds  per  square  foot) 
has  a  decided  advantage  in  the  preparation  of  designs  for 
competition,  as  all  bidders  are  working  upon  the  same 
basis.  Theoretically,  for  the  wind  itself  the  pressure 
per  square  foot  is  to  be  preferred  and  the  force  that  pro- 
duces lateral  vibration  is  best  represented  by  a  percentage 

*Robinson,  "Vibration  of  Bridges."  Trans.  Amer.  Soc. 
C.  E.,  Vol.  XVI,  p.  42. 

fReichman,  "Journal  of  the  Western  Soc.  of  Eng's,"  Vol. 
29,  p.  93. 

[  35  ] 


of  the  moving  load.  As  engine  weights  and  car  loads  are 
increased,  provision  is  thus  made  for  the  increased  ten- 
dency to  vibration.  Again,  a  different  lateral  force  for 
spans  under  200  ft.  from  that  for  spans  over  200  ft.  is  as- 
sumed by  some  engineers. 

While  the  wind  pressure  on  a  moving  train  should  be 
treated  as  a  moving  load,  engineers  are  divided  in  their 
opinions  as  to  the  wind  load  on  the  structure  itself ;  some 
considering  it  uniform  and  some  moving. 

In  regard  to  end  anchorage,  the  following  will  be  quoted 
from  Waddell's  "De  Pontibus" :  "No  matter  how  great 
its  weight  may  be,  every  ordinary  fixed  span  should  be 
anchored  effectively  to  its  support  at  each  bearing  on 
same."  (Principle  XXVI,  in  chapter  "First  Principles  of 
Designing.") 

In  passing,  a  criticism  will  be  launched  at  the  Eng- 
lish bridges  of  "an  early  Victorian  type,"*  having  an 
arched  portal  strut  at  every  post  and  no  top  laterals. 
Some  of  these  are  of  late  date.  All  are  wasteful  in  mater- 
ial, and  there  is  great  ambiguity  in  regard  to  the  lateral 
stresses. 

PRESENT  SPECIFICATIONS 

The  specifications  of  the  American  Eailway  Engineer- 
ing Association,  1910,  read : 

All  spans  shall  be  designed  for  a  lateral  force  on  the  loaded 
chord  of  200  Ib.  per  lin.ft.  plus  10%  of  the  specified  train  load 
on  one  track,  and  200  Ib.  per  lin.ft.  on  the  unloaded  chord; 
these  forces  being  considered  as  moving. 

The  American  Bridge  Co.  or  Schneider  specifications 
assume  the  wind  pressure : 

First,  at  30  Ib.  per  sq.ft.  on  the  exposed  surface  of  all 
trusses  and  the  floor  as  seen  in  elevation,  in  addition  to  a 
train  of  10  ft.  average  height,  beginning  2  ft.  6  in.  above 
base  of  rail,  moving  across  the  bridge.  Second,  at  50  Ib. 
per  sq.  ft.  on  the  exposed  surface  of  all  trusses  and  the  floor 
system.  The  greatest  result  shall  be  used  in  proportioning 
the  parts. 

The  Cooper  specifications  call  for  provision  to  be  made 
to  resist  a  lateral  force  of  600  Ib.  per  lin.ft.  on  the  loaded 
chord,  of  which  450  Ib.  is  to  be  treated  as  a  moving  load 
acting  on  a  train  of  cars  at  a  line  6  ft.  above  base  of  rail. 

*The   Tugela   Bridge,   "Engineering,"   Jan.    26,   1900. 

[36] 


The  unloaded  chord  is  to  resist  a  lateral  force  of  200  Ib. 
per  lin.ft.  for  spans  up  to  200  ft.,  and  25  Ib.  for  each  ad- 
ditional 50  ft. 

The  specifications  of  the  railroads  mentioned  below  are 
selected  from  a  larger  number  to  show  the  varying  assump- 
tions made  of  the  amount  of  wind  and  lateral  forces  to  be 
used  in  the  design  of  railroad  bridges.  The  wind  is  as- 
sumed to  act  horizontally  at  right  angles  to  the  bridge. 
Pounds  per  lineal  foot  means  lineal  foot  of  bridge. 

Baltimore  &  Ohio  R.R.  Co. — A  moving  lateral  force  of  600 
Ib.  per  lin.ft.  against  the  loaded  chord,  and  200  Ib.  per  lin.ft. 
against  unloaded  chord. 

Buffalo,    Rochester    &    Pittsburgh     Ry.     Co. — (a)      On     the 

loaded  structure,  30  Ib.  per  sq.ft.  on  the  exposed  surface  of 
all  trusses  and  the  floor  system  as  seen  in  elevation,  and  on 
a  moving  train  surface  of  10  ft.  average  height  beginning 
2  ft.  6  in.  above  base  of  rail,  (b)  On  the  unloaded  structure, 
50  Ib.  per  sq.ft.  (instead  of  30).  In  no  case  shall  a  lateral 
force  of  less  than  200  Ib.  fixed  and  300  Ib.  moving  per  lin.ft. 
be  used  for  the  loaded  chord  and  less  than  150  Ib.  per  lin.ft. 
fixed  for  the  unloaded  chord. 

Canadian  Pacific  Ry.  Co. — Same  as  the  Schneider  specifica- 
tions. 

Chesapeake  &  Ohio  Ry.  Co. — Against  the  unloaded  chord 
a  fixed  force  of  200  Ib.  per  lin.ft.  for  all  spans  of  200  ft. 
and  under,  and  an  additional  force  of  10  Ib.  per  lin.ft.  for 
every  25  ft.  increase  in  span  over  200  ft.  Against  the  loaded 
chord  same  as  above  with  an  additional  force  of  500  Ib. 
per  lin.ft.  acting  8  ft.  above  base  of  rail  and  treated  as  a 
moving  load. 

Chicago,  Milwaukee  &  St.  Paul  Ry.  Co. — A  lateral  force  of 
750  Ib.  per  lin.ft.  against  the  loaded  chord,  and  200  Ib.  per 
lin.ft.  against  the  unloaded  chord,  these  forces  being  consid- 
ered as  moving. 

Delaware  &  Hudson  Co. — For  the  loaded  chord  300  Ib.  per 
lin.ft.  moving  load  and  200  Ib.  per  lin.ft.  dead-load.  For  the 
unloaded  chord,  200  Ib.  per  lin.ft.  dead-load.  For  double-track 
bridges  these  loads  shall  be  increased  one-half. 

Delaware,  Lackawanna  &  "Western  R.R. — A  moving  load 
of  300  Ib.  per  lin.ft.  against  the  loaded  chord,  and  a  uniform 
load  of  300  Ib.  per  lin.ft.  divided  equally  between  loaded  and 
unloaded  chords. 

Grand  Trunk  Railway  System  has  "Private"  printed  on  the 
title  page  of  its  specifications  and  hence  they  can  not  be 
quoted. 

Harrimnii  Lines — Same  wording  as  Buffalo,  Rochester  & 
Pittsburgh  Ry.  Co.  above. 

Lehigh  Valley  R.R.  Co. — A  moving  load  of  700  Ib.  per  lin.ft. 
against  the  loaded  chord  and  a  moving  load  of  300  Ib.  per 
lin.ft.  against  the  unloaded  chord. 

Long  Island  R.R.  Co. — (1st)  A  load  of  30  Ib.  per  sq.ft. 
"on  the  exposed  surface  of  entire  surface  as  seen  in  elevation" 
(but  never  less  than  200  Ib.  per  lin.ft.  at  the  unloaded  chord), 
and  on  a  moving  train  10  ft.  high  beginning  2  ft.  5  in.  above 
base  of  rail;  (2d)  50  Ib.  per  sq.ft.  on  "the  exposed  surface  of 
the  entire  structure  as  seen  in  elevation." 

Mexican  International  R.R.  Co. — Six  hundred  pounds  per 
lineal  foot  against  the  loaded  chord  and  200  Ib.  per  lin.ft. 
against  the  unloaded  chord,  both  forces  considered  as  moving. 

National  Lines  of  Mexico — On  the  unloaded  structure  50  Ib. 
per  sq.ft.  "on  the  geometrical  elevation  of  the  completed 
structure  and  track."  On  the  loaded  structure,  "30  Ib.  per 
sq.ft.  of  said  elevation,"  plus  the  moving  surface  of  train  10 


[37] 


ft.  high,  beginning  2%  ft.  above  the  base  of  rail.  In  no  case 
shall  the  fixed  wind  pressure  be  less  than  150  Ib.  per  lin.ft. 
for  each  chord  of  any  bridge. 

New  York  Central  Lines— (1st)  A  moving  load  of  30  Ib. 
per  sq.ft.  on  1%  times  the  vertical  projection  of  the  structure 
on  a  plane  parallel  with  its  axis  (but  never  less  than  200  Ib. 
per  lin.ft.  at  the  unloaded  chord),  and  a  moving  load  of  360 
Ib.  per  lin.ft.  applied  8  ft.  above  the  base  of  the  rail.  (2d)  A 
moving  load  of  50  ft.  per  sq.ft.  on  1%  times  the  vertical  pro- 
jection of  the  unloaded  structure  on  a  plane  parallel  with  its 
axis. 

New  York,  New  Haven  &  Hartford  R.R.  Co. — Same  as  the 

A.  R.  E.  Assn. 

New  York,  Ontario  &  Western  Ry.  Co. — Same  as  the  A.  R. 

B.  Assn.     For  double-track  bridges  the  constants  are  increased 
50%  but  the  percentage  of  live-load  remains  the  same. 

Norfolk  &  "Western  Ry.  Co. — Same  as  the  Schneider  speci- 
fications, but  omitting  "beginning  2  ft.  6  in.  above  base  of 
rail." 

Pennsylvania  R.R.  Co. — Same  as  the  Schneider  specifica- 
tions. 

Pennsylvania  Lines  West  of  Pittsburgh — A  uniform  load 
of  150  Ib.  per  lin.ft.  against  the  unloaded  chord  and  200  Ib. 
per  lin.ft.  against  the  loaded  chord.  A  moving  load  of  300 
Ib.  per  lin.ft.  against  the  loaded  chord  acting  at  a  line  6  ft. 
above  the  base  of  rail. 

Philadelphia  &  Reading:  Ry.  Co. — A  uniform  load  of  200 
Ib.  per  lin.ft.  against  each  chord  and  a  moving  load  of  400 
Ib.  per  lin.ft.  against  the  loaded  chord  with  its  point  of  appli- 
cation iy2  ft.  above  the  rail. 

Piedmont  &  Northern  Lines — Same  as  A.  R.  E.  Assn. 

Seaboard  Air  Line  Ry. — Same  as  A.  R.  E.  Assn. 

Southern  Ry.   Co. — Same   as  A.   R.   E.   Assn. 

Western  Maryland  Ry.  Co. — Dead-load,  150  Ib.  per  lin.ft. 
against  the  unloaded  chord,  and  200  Ib.  per  lin.ft.  against  the 
loaded  chord.  Moving  load,  400  Ib.  per  lin.ft.  against  the 
loaded  chord,  applied  at  a  distance  of  6  ft.  above  the  base 
of  rail. 

Western   Pacific   Ry.   Co. — Same   as   Western   Maryland. 

The  wide  range  of  requirements  demanded  in  exist- 
ing specifications  shows  the  difficulty  of  uniting  on  a  com- 
mon standard.  At  present  an  increasing  number  of 
railroad  engineers  is  following  the  specifications  of  the 
American  Eailway  Engineering  Association.  In  Europe, 
bridges  are  built  in  accordance  with  rules  and  regulations 
prepared  by  the  respective  governments.  This  at  times  is 
an  advantage,  at  other  times  it  is  not.  Unwin  writes: 
'English  bridge  builders  are  somewhat  hampered  in  adopt- 
ing rational  limits  of  working  stresses  by  the  rules  of  the 
Board  of  Trade." 

WORKING  STRESSES 

The  required  material  in  a  bridge  depends  upon  as- 
sumed unit  stresses  as  well  as  upon  assumed  loadings. 
Some  ten  years  ago,  the  late  Professor  Heller*  found  that 
for  the  same  live-  and  dead-load  stresses  in  a  bottom- 

*"Engineering  News,"  Nov.  19,  1903. 

[38] 


chord  member  of  a  134-ft.  span,  there  was  a  variation 
from  11.4%  below  to  18.6%  above  the  average  section  of 
25.4  sq.in.  required  by  the  28  specifications  he  examined. 
In  the  specifications  of  the  25  railroads  mentioned  above, 
with  the  total  stresses  assumed  by  Heller,  the  variation 
is  from  11.65%  below  to  9.33%  above  the  average  of 
24.97  sq.in.  required.  There  is  nearly  a  unanimity  in 
using  for  the  combined  stress  due  to  lateral  forces,  plus 
live-  and  dead-loads,  a  unit-stress  25  or  30%  greater 
than  that  due  to  the  live-  and  dead-loads  alone. 

In  this  connection  attention  is  called  to  the  bending 
stresses  in  the  end  posts  due  to  portal  bracing;  and  the 
stresses  induced  in  different  members  when  the  bridge 
is  figured  for  overturning  moments.  These  are  not  to 
be  neglected,  nor  are  centrifugal  stresses  when  track  is 
on  curve. 

LONG  SPANS 

What  has  been  written  and  the  specifications  quoted 
apply  primarily  to  railroad  bridges  of  noncontinuous  truss 
spans.  When  the  Ohio  Eiver  bridge  between  Cincinnati 
and  Covington  was  finished  in  1889  with  a  center  span 
of  545  ft.  and  two  spans  of  486  ft.,  it  had  the  distinction 
of  having  the  longest  and  heaviest  simple  truss  that  had 
been  built  either  in  the  United  States  or  in  Europe.  The 
specifications  called  for  a  wind  pressure  of  30  Ib.  per  sq.ft. 
on  the  exposed  surface  of  both  trusses  and  the  vertical 
projection  of  the  floor  system,  and  on  a  moving-train  sur- 
face averaging  10  sq.ft.  per  lin.ft. 

The  St.  Louis  Municipal  Bridge  has  three  spans,  each 
of  668  ft.  center  to  center  of  end  pins,  at  present  the 
longest  simple  truss  spans  in  the  world.*  The  permissible 
lengths  of  the  spans  are  explained  by  58%  of  the  metal 
being  nickel-steel.  The  wind  loads  assumed  were  300 
Ib.  per  lin.ft.  for  the  upper  lateral  system,  and  600  Ib.  per 
lin.ft.,  one-half  moving  and  one-half  fixed,  for  the  lower 
lateral  system. 

*Merriman  and  Jacoby  in  the  last  edition  of  their  "Roofs 
and  Bridges"  enumerate  31  railway  bridges  and  6  combined 
railway  and  highway  bridges  which  have  simple  truss  spans 
of  400  ft.  and  over  in  length.  Of  these  15  are  over  500  ft. 
and  two,  including  the  St.  Louis  bridge,  are  over  600  ft. 
The  new  Ohio  River  Bridge  at  Metropolis,  recently  contracted 
for,  has  a  noncontinuous  channel  span  of  700  ft.  clear  distance 
between  piers. 

[  39  ] 


The  Hell  Gate  Bridge,  now  building,  will  have  the  long- 
est arch  in  the  world — a  span  of  977^  ft.  The  para- 
graph in  the  specifications  relating  to  wind  pressure  reads : 

Wind,  pressure  shall  be  assumed  as  a  moving  load  of  500 
Ib.  per  lin.ft.  in  the  plane  of  the  tracks,  plus  30  Ib.  per  sq.ft. 
on  such  vertical  surface  of  the  unloaded  bridge  as  shall  be 
exposed  at  any  angle  between  20°  above  or  20°  below  the 
horizontal  or  at  an  angle  of  45°  from  the  axis  of  the  bridge, 
but  not  less  than  200  Ib.  per  lin.ft.  on  any  chord. 

For  25  years  the  Forth  Bridge  of  cantilever  design, 
in  Scotland,  has  remained  the  greatest  bridge  in  the 
world.  Its  spans  of  1700  ft.  exceed  in  length  and  magni- 
tude any  other  now  standing.  The  wind  loads  and  unit 
stresses  used  in  the  design  were  those  of  the  English  Board 
of  Trade  Eegulations,  which  most  engineers  regard  as  ex- 
cessive and  needlessly  severe.  The  table  below,  made  by 
Sir  Benjamin  Baker  from  his  calculations  of  stresses  due 
to  the  separate  loadings,  will  show  the  important  part 
wind  forces  played  in  the  design. 

Dead  Live 

Load  Load  Wind  Total 

Stresses  Stresses  Stresses  Stresses 

Bottom  member   .                         2282  1022  2920  6224 

Top  member 2253  997  544  3794 

Vertical  member 1550  705  1024  3279 

Diagonal   struts    802  167  414  1383 

Diagonal    ties    754  186  194  1134 

Horizontal   wind  bracing. .          80                  5  265  350 

Vertical  wind  bracing 42  169  108  319 

Central  girder— top 337  303  182  822 

Central  girder — bottom    . . .        330  301  247  878 
Stresses  are  given  in  tons  of  2240  Ibs. 

The  Quebec  Bridge,  also  of  cantilever  design,  now 
building,  will,  when  finished,  eclipse  the  Forth  Bridge, 
its  enormous  channel  span  being  1800  ft.  long.  The  as- 
sumed wind  loads  are: 

A  wind  load  normal  to  the  bridge  of  30  Ib.  per  sq.ft.  of  the 
exposed  surface  of  two  trusses  and  1%  times  the  elevation 
of  the  floor  (fixed  load),  and  also  30  Ib.  per  sq.ft.  on  travelers 
and  falsework,  etc.  during  erection. 

A  wind  load  on  the  exposed  surface  of  the  train  of  300 
Ib.  per  lin.ft.  applied  9  ft.  above  base  of  rail  (moving  load). 

A  wind  load  parallel  with  the  bridge  of  30  Ib.  per  sq.ft. 
acting  on  one-half  the  area  assumed  for  normal  wind  pressure. 

CONCLUSION 

The  writer  has  no  intention  of  passing  judgment  upon 
the  specifications  of  engineers  who  have  carried  American 
bridge  building  to  such  a  marked  success.  Standard  speci- 
fications, as  far  as  wind  stresses  are  concerned,  may  not 


[40  ] 


be  practicable,  but  it  should  be  possible  to  come  nearer  to 
points  of  agreement  than  at  present.  As  an  instance,  the 
Lehigh  Valley,  the  Philadelphia  &  Heading,  and  the  Lack- 
awanna  railroads,  all  in  the  same  territory,  must  have 
practically  the  same  lateral  forces ;  but  the  assumed  forces 
vary  nearly  75%.  A  discussion  of  the  reasons  for  these 
variations  would  be  interesting. 

In  no  specifications  that  the  writer  has  ever  read  is 
there  an  attempt  to  separate  the  stresses  due  to  wind 
from  those  due  to  other  lateral  forces.  The  10%  of  the 
weight  of  the  train  often  specified  for  the  lateral  force 
on  the  loaded  chord  includes  the  wind  pressure  on  the 
train.  The  wind  pressure  of  30  Ib.  per  sq.ft.  on  a  mov- 
ing train,  sometimes  called  for,  includes  the  lateral  force 
due  to  vibration.  When  the  assumed  loading  is  given  in 
Ib.  per  lin.ft.,  the  total  pressure  due  to  all  lateral  forces 
is  intended. 

Perhaps  in  the  future  some  engineer  may  be  able  to 
assign  definite  amounts  to  the  different  items  that  make 
up  the  total  lateral  force  on  a  bridge.  This  would  be  one 
of  the  first  steps  to  be  taken  to  secure  any  degree  of  uni- 
formity in  proposed  requirements  for  lateral  stresses.  As 
a  beginning  in  this  direction,  the  writer  suggests  that  the 
lateral  force  on  the  loaded  chord  due  to  oscillation  of 
the  train  be  taken  at  4%  of  the  train  load. 


[41] 


IV 

Wind  Stresses  in  Highway 
Bridges 

SYNOPSIS — A  review  of  the  varying  assump- 
tions that  have  been  made  regarding  the  wind 
stresses  in  highway  bridges.  Problem  complicated 
by  lateral  forces  due  to  traffic.  Present-day  spec- 
ifications, and  variation  of  practice. 

EARLY  AMERICAN  WRITERS 

WHIPPLE — In  the  early  part  of  1847  there  appeared 
a  pamphlet  of  48  pages  with  the  title,  "An  Essay  on 
Bridge  Building,  containing  analyses  and  comparisons 
of  the  principal  plans  in  use,  with  investigations  as  to 
the  best  plans  and  proportions,  and  relative  merits  of 
wood  and  iron,  for  bridges.  By  S.  Whipple,  C.  E.,  Mathe- 
matical and  philosophical  instrument  maker.  Utica,  N.  Y. 
H.  H.  Curtiss,  printer,  Devereux  Block,  1847."  After  dis- 
tributing 50  or  60  copies  among  friends,  the  author  bound 
the  remainder  of  the  edition  with  "Essay  No.  II  on 
Bridge-Building  Giving  Practical  Details  and  Plans  for 
Iron  and  Wooden  Bridges/'  which  he  had  written  and 
printed  later  in  the  year.  This  little  book  of  120  pages 
and  10  plates  was  the  pioneer  in  the  mathematics  of 
bridge  construction.  To  Squire  Whipple,  its  author,  the 
inventor  of  the  Whipple  bridge,  belongs  the  honor  of 
being  the  first  to  publish  a  correct  analysis  of  the  stresses 
in  a  simple  truss.  His  work  did  not  become  widely 
known.  In  1869  he  took  the  copies  remaining  of  his 
original  edition  and  bound  them  "with  an  appendix,  con- 
taining Corrections,  Additions  &  Explanations,  Sug- 
gested by  Subsequent  Experience :  to  which  is  annexed  an 
Original  Article  on  the  doctrine  of  Central  Forces."  This 
addition  of  about  150  pages  the  author  prepared  and 
printed  with  his  own  hands. 

In  1872  an  enlarged  and  rewritten  edition  was  pub- 
lished by  the  D.  Van  Nostrand  Co.  In  1873  a  chapter 

[  43  ] 


of  35  pages  on  Drawbridges  was  added.  From  a  copy 
of  this  1873  edition,  the  following  quotations  regarding 
swaybracing  are  taken. 

The  primary  and  essential  purpose  of  a  bridge  is  to  with- 
stand vertical  forces  which  are  certain  and,  to  a  large  extent, 
determinate  in  amount But  the  lateral  or  trans- 
verse forces  to  which  a  bridge  superstructure  is  liable,  are  of 
a  casual  nature,  depending  upon  conditions  of  which  we  have 
only  a  vague  and  general  knowledge;  ....  But  in  ar- 
ranging his  system  for  securing  lateral  stability  and  steadi- 
ness, science  can  lend  him  but  little  assistance He 

knows  the  wind  will  blow  against  the  side  of  his  structure, 
but  whether  with  a  maximum  force  of  one  hundred  pounds,  or 
as  many  thousands,  he  has  no  means  of  knowing  with  any 
considerable  degree  of  certainty  or  probability  ....  No 
attempt  will  be  made  here  to  assign  specific  stresses  as  liable 
to  occur  in  sway  rods  or  braces,  based  upon  calculations  from 
the  uncertain  and  indeterminate  elements  upon  which  the 
lateral  action  upon  bridges  depends.  But  judging  from  ex- 
perience and  observation,  it  may  be  recommended  that  iron 
sway  rods  be  made  of  iron  not  less  than  %  inch  in  diameter, 
for  bridges  of  five  panels  or  under,  %-in.  from  six  to  ten 
panels  inclusive.  For  twelve  and  fourteen  panels,  %-in.  for 
ten  middle  panels  and  %-in.  for  the  rest;  and  for  sixteen  the 
same  as  last  above,  with  the  addition  of  a  pair  of  1-in.  rods  in 
the  end  panels. 

These  are  opinions  from  the  father  of  modern  bridge 
building,  written  only  42  years  ago. 

BOLLER — Boiler's  "Iron  Highway  Bridges/'  first  pub- 
lished in  1876,  which  has  passed  through  several  editions, 
says, 

The  horizontal  or  sway  bracing  may  consist  of  very  light 
rods,  if  the  floor  is  well  laid,  forming  as  it  does  a  very  effec- 
tive system  of  bracing  against  lateral  movement.  Rods  from 
%-  to  1-in.  round  will  cover  all  but  extreme  requirements,  and 
they  are  attached  by  any  convenient  means  to  the  floor- 
beams  near  their  point  of  support. 

In  modern  textbooks  calculation  has  taken  the  place  of 
speculation.  Most  of  what  has  been  written  about  the 
wind  stresses  in  railroad  bridges*  applies  to  highway 
bridges.  The  same  questions  of  the  intensity  of  wind 
pressure  per  unit  of  area  exposed,  and  the  amount  of  area 
to  be  considered  as  exposed  surface,  are  to  be  met.  In- 
duced stresses,  load  uniform  or  moving,  and  lateral  forces 
other  than  wind  are  also  to  be  considered. 


*In   the  preceding  article. 

[44] 


CHANGED  TRAFFIC  KEQUIBEMENTS 
The  whole  subject  of  loadings  on  highway  bridges  is 
being  revised.  This  is  the  day  of  heavy  concentrated 
loads.  Many  present  bridges  are  seriously  overloaded 
by  the  traffic  coming  upon  them,  especially  in  the  floor- 
beams  and  joists.  They  were  often  built  to  carry  uni- 
form live-loads  of,  say  125  Ib.  per  sq.ft.  for  the  floor-beams 
and  80  or  100  Ib.  for  the  trusses.  Sometimes  a  road  roller 
was  mentioned  in  the  specifications.  Manufacturers  are 
constantly  increasing  the  weight  of  road  rollers  and  trac- 
tion engines,  and  with  the  good-roads  movement  many 
bridges  are  called  upon  to  carry  rollers  and  engines  for 
which  they  were  not  designed.  Then  there  is  the  automo- 
bile, often  run  at  a  speed  of  30  mi.  per  hr. 

But  the  severest  tests  to  which  some  of  our  highway 
bridges  are  being  put  are  those  from  the  auto  trucks.** 
The  traffic  of  towns  and  cities  now  reaches  far  out  into  the 
country.  The  road  roller  runs  slowly,  while  the  auto 
truck  may  be  driven  at  a  speed  of  12  mi.  per  hr.  and  two 
trucks  may  meet  or  pass  each  other  on  the  same  bridge. 
A  load  of  10  tons  is  often  carried  and  the  weight  of 
the  truck  adds  another  6  tons.  (In  New  York  City  a  load 
of  75  tons  has  been  carried  on  a  truck  weighing  10  tons, 
most  of  the  load  being  on  the  two  rear  wheels.)!  Trucks 
are  being  made  heavier  and  with  increased  capacity. 
Greater  impact  stresses  are  induced  and  the  tendency  to 
both  vertical  and  lateral  vibration  becomes  greater.  Some- 
times centrifugal  forces  are  introduced.  AH  this  is  par- 
ticularly true  of  the  auto  truck  when  fully  loaded  and 
with  a  driver  ignorant  or  indifferent  to  loadings,  speed,, 
and  the  strength  of  bridges.  One  writer,J  however,  does 
not  think  the  vibration  effects  greater  than  those  produced 
by  a  horse  and  wagon.  Anyone  who  has  stood  on  a  coun- 
try bridge  of  150-ft.  span  while  a  horse  drawing  a  light 
buggy  was  crossing  at  a  trot  may  have  felt  a  decided  jolt- 
ing of  the  whole  structure,  a  condition  largely  remedied 
by  rigid  connections  and  stiff  members. 


**Motor     Truck     Loading     on     Highway     Bridges      "Entr 
News,"  Sept.   3,   1914. 

tSeaman,  Proceedings,  Am.  Soc.  C.  E.,  December,  1911. 
JNeff  (Am.  Assoc.  for  Advancement  of  Science),  "Enerineer- 
ing  and  Contracting,"  Jan.  22,  1913. 

[45] 


Electric-car  lines  are  being  extended,  and  cars  are  be- 
ing increased  in  weight  and  run  at  greater  speed.  When 
a  highway  bridge  carries  electric  cars  it  becomes  in  real- 
ity a  miniature  railroad  bridge.  City  or  county  officials 
who,  without  examination  by  a  competent  engineer,  will 
sanction  the  use  of  existing  bridges  to  carry  electric  cars, 
belong  to  the  class  of  undesirable  citizens. 

LATERAL  FORCES  OTHER  THAN  WIND  PRESSURE 

The  assumed  wind  load  in  bridge  specifications  includes 
all  the  lateral  forces  whether  so  stated  or  not.  The  writer 
believes  that  this  is  sufficient  (in  nearly  all  present  speci- 
fications) to  take  care  of  the  increased  lateral  forces  due 
to  changed  traffic  requirements.  With  the  exception  of 
the  electric  car,  it  is  improbable  that  the  full  wind  load 
will  be  acting  at  the  same  time  that  the  lateral  vibration 
occurs,  due  to  the  moving  load.  It  should  be  remembered 
that,  if  by  any  means  a  highway  bridge  is  blown  over, 
there  is  not  likely  to  be  any  loss  of  life,  neither  will  traf- 
fic be  seriously  interrupted.  The  actual  loss  to  the  au- 
thorities is  little  more  than  the  cost  of  the  structure  it- 
self. Hence,  excessive  bracing  in  all  bridges  to  guard 
against  a  remote  possibility  in  a  single  one  is  unneces- 
sarily expensive.  With  a  railroad  bridge  it  is  differ- 
ent; provision  must  there  be  made  for  remote  possi- 
bilities. 

The  weakness  of  lateral  systems  of  highway  bridges  in 
the  past  has  not  been  so  much  in  the  assuming  of  loads 
as  in  the  abominable  details  used.  Witness  the  common 
practice  of  25  years  ago  and  still  prevalent  in  some  quar- 
ters of  fastening  the  lower  laterals  in  a  nondescript  way 
to  the  floor-beams,  which,  in  turn,  are  suspended  from  the 
pins  by  U-bolt  hangers;  or,  the  top  laterals  having  bent 
eyes  taking  the  top-chord  pins  and  pulling  against  struts 
attached  to  the  same  pins  by  bent  plates.  It  is  better  to 
design  for  a  safe  and  sane  wind  loading,  taking  care 
of  induced  stresses,  and  with  all  details  fully  up,  than  to 
proportion  the  body  of  the  lateral  members  for  larger 
stresses  and  use  inefficient  details. 

In  high-truss  bridges  the  compression  chord  is  kept  in 
alignment  by  the  top  lateral  system.  In  the  pony  truss, 

[46] 


recourse  is  often  had  to  doubtful  expedients.  "One  has 
only  to  shake  the  top  chord  of  a  pony  truss  to  see  how 
loosely  it  is  secured  laterally  and  to  demonstrate  its  lack 
of  fixity  at  intermediate  points."*  With  the  moving  loads 
now  coming  into  use,  the  pony  truss  is  doomed.  In  some 
specifications  it  is  prohibited  altogether. 

The  wind  is  generally  assumed  to  blow  horizontally,  but 
it  may  vary  greatly  from  the  horizontal.  For  high  bridges 
in  exposed  localities,  the  upward  pressure  should  be  taken 
into  account;  the  end  anchorage  should  provide  for  any 
possible  uplift  and  against  the  structure  being  moved  off 
its  seats  either  by  wind  pressure  or  by  a  blow  from  a 
passing  object.  A  study  of  the  wreck  of  the  High  Bridge 
over  the  Mississippi  River  at  St.  Paulf  is  interesting. 

PRESENT  SPECIFICATIONS 

SCHNEIDER — Passing  to  well  known  specifications,  the 
American  Bridge  Co.  or  Schneider  specifications  for  steel 
highway  bridges  read : 

The  wind  pressure  shall  be  assumed  acting  in  either  di- 
rection horizontally: 

First.  At  30  Ib.  per  sq.ft.  on  the  exposed  surface  of  all 
trusses  and  the  floor  as  seen  in  elevation,  in  addition  to  a 
horizontal  live-load  of  150  Ib.  per  lin.ft.  of  the  span  moving 
across  the  bridge,  but  not  less  than  300  Ib.  per  lin.ft.  shall 
be  used  for  bracing  of  loaded  chord  nor  less  than  150  Ib.  per 
lin.ft.  of  unloaded  chord. 

Second.  At  50  Ib.  per  sq.ft.  on  the  exposed  surface  of  all 
trusses  and  the  floor  system. 

The  greatest  result  shall  be  assumed  in  proportioning  the 
parts. 

COOPER — Probably  more  highway  bridges  have  been 
built  in  accordance  with  the  specifications  of  Theodore 
Cooper  than  any  other.  The  paragraphs  stating  amount 
of  lateral  forces  are: 

To  provide  for  wind  and  vibrations,  the  top  lateral  brac- 
ing in  deck  bridges  and  the  bottom  lateral  bracing  in  through 
bridges  shall  be  proportioned  to  resist  a  lateral  force  of  300 
Ib.  for  each  foot  of  the  span;  150  Ib.  of  this  to  be  treated  as  a 
moving  load. 

The  bottom  lateral  bracing  in  deck  bridges  and  the  top 
lateral  bracing  in  through  bridges  shall  be  proportioned  to 
resist  a  lateral  force  of  150  Ib.  for  each  foot  of  the  span. 

For  spans  exceeding  300  ft.,  add  in  each  of  the  above  cases 
10  Ib.  additional  for  each  additional  30  ft. 

Johnson,  Bryan  &  Turneaure;  Merriman  &  Jacoby; 
Ketchum;  and  others  in  their  textbooks  follow  Cooper's 
specifications  regarding  wind  pressure.  Others,  as  Mar- 

*Smith,  Proceedings,  Indiana  Eng.  Soc.,  1911,  p.  209;  "En- 
gineering Record,"  Jan.  21,  1911. 

tTurner,  Trans.  Am.  Soc.  C.  E.,  June,  1905,  Vol.  LJV,  p.  31. 

[47] 


burg,  and  Burr  &  Falk,  quote  both  the  Schneider  and  the 
Cooper  specifications. 

WADDELL — Waddell  in  his  "Ordinary  Highway 
Bridges"  assumes  a  wind  pressure  of  40  Ib.  per  sq.ft.  for 
spans  100  ft.  and  under,  35  Ib.  for  spans  100  to  150  ft., 
and  30  Ib.  for  spans  greater  than  150  ft. ;  these  pressures 
to  be  increased  10  Ib.  for  bridges  in  unusually  exposed  lo- 
cations. The  loads  are  considered  moving. 

The  total  area  opposed  to  the  wind  is  to  be  determined  by 
adding  together  the  area  of  the  vertical  projection  of  the  floor 
and  joists,  and  twice  the  area  of  the  vertical  projection  of 
the  windward  truss,  hub  plank,  guard  rail,  and  ends  of  floor- 
beams. 

In  his  "Specifications  for  Steel  Highway  Bridges," 
1906,  the  wind  loads  per  lineal  foot  of  span  for  both  the 
loaded  and  unloaded  chords  are  taken  from  curves  shown 
on  a  diagram.  The  diagram  was  figured  (for  a  clear 
roadway  of  20  ft.)  with  intensities  varying  from  40  Ib. 
for  very  short  spans  to  25  Ib.  for  very  long  ones.  For 
spans  up  to  600  ft.,  the  curves  show  loads  from  200  to  355 
Ib.  per  lin.ft.  of  bridge  on  the  loaded  chord  and  100  to 
265  Ib.  on  the  unloaded  chord,  according  to  the  length 
of  span  and  the  class  of  the  bridge.  For  wider  struc- 
tures, the  wind  loads  are  to  be  increased  2%  for  each 
foot  of  width  in  excess  of  20  ft. 

GREINEK — The  "Specifications  for  Steel  Stationary 
Bridges,"  by  Greiner,  require  that 

for  city,  interurban  and  country  bridges  the  lateral  force 
against  unloaded  chords  shall  be  assumed  not  less  than 
150  Ib.  per  lin.ft.  plus  10%  of  the  uniform  load  on  one  car 
track  or  on  a  width  of  12  ft.,  and  for  the  unloaded  chords  150 
Ib.  per  lin.ft.  In  cases  where  a  lateral  force  of  30  Ib.  per 
sq.ft.  on  1%  times  the  vertical  projection  of  the  structure 
produces  greater  stresses  than  the  above  loads,  it  shall  be 
considered.  All  lateral  loads  shall  be  treated  as  moving. 

OSTRUP — Ostrup,  in  his  "Standard  Specifications  for 
Highway  Bridges/'  calls  for  wind  bracing  to  be  designed 
to  resist  one  of  the  following  lateral  loadings,  whichever 
produces  the  greater  stress:  (a)  Structure  unloaded,  50 
Ib.  per  sq.ft.  on  the  exposed  surface  of  all  trusses  and  the 
floor  as  seen  in  elevation;  or  (b)  Structure  loaded, 
bridges  (of  all  classes)  carrying  highway  traffic  only,  30 
Ib.  per  sq.ft.  on  the  exposed  surface  of  all  trusses  and 
the  floor  as  seen  in  elevation  in  addition  to  a  uniform 

[48  ] 


load  of  150  Ib.  per  lin.ft.  of  structure  applied  on  the 
loaded  chord;  or  (c)  Structure  loaded,  bridges  of  all 
classes  carrying  electric-railway  traffic,  the  same  loading 
as  under  (b)  except  that  the  additional  uniform  load  is 
300  Ib.  per  lin.ft.  of  structure  and  is  applied  7  ft.  above 
the  base  of  rail.  The  minimum  value  of  the  pressure  is 
to  be  250  Ib.  per  lin.ft.  for  the  loaded  and  150  Ib.  for  the 
unloaded  chord  of  the  structure. 

BOWSER — Bowser,  in  a  "Treatise  on  Eoofs  and 
Bridges,"  gives  30  Ib.  per  sq.ft.  of  exposed  surface  of  both 
trusses  as  the  maximum  wind  load  upon  a  highway  bridge. 
To  estimate  the  30-lb.  pressure  when  the  surface  is  not 
known,  he  writes,  "it  is  customary  to  use  the  following 
rule :  Take  150  Ib.  per  lin.ft.  per  truss,  or  75  Ib.  per  lin. 
ft.  for  each  chord." 

MEREIMAN — In  the  earlier  editions  of  Merriman's 
work,  "A  Textbook  on  Eoofs  and  Bridges/'  are  found  the 
sentences : 

For  a  highway  bridge  the  surface  exposed  to  wind  action 
is  usually  taken  as  double  the  side  elevation  of  one  truss.  If 
the  area  of  this  be  not  known,  an  approximation  to  its  value 
may  be  found  by  taking  it  as  many  square  feet  as  there  are 
linear  feet  in  the  skeleton  outline  of  the  truss. 

A  number  of  the  states,  through  highway  commission- 
ers or  otherwise,  have  issued  specifications  for  steel  high- 
way bridges.  Some  of  them  are  incomplete  and  written 
by  men  without  a  clear  knowledge  of  the  subject.  Below 
are  given  quotations  from  these  and  some  other  sources, 
as  to  horizontal  wind  pressure. 

COLORADO — 300  Ib.  per  lin.ft.  on  the  loaded  chord  and 
150  Ib.  per  lin.ft.  on  the  unloaded  chord. 

ILLINOIS  —  Cooper's  Specifications  for  Highway  Bridges, 
ed.  of  1909,  "except  as  hereinafter  specified  or  as  may  be 
specially  indicated  on  the  drawings." 

MICHIGAN — No  mention  made  of  wind  loads  but  they  may 
be  covered  by  the  paragraph,  "Any  questions  that  may  arise 
as  to  the  quality  of  material  and  labor  shall  be  settled  in 
accordance  with  the  provisions  of  Theodore  Cooper's  Specifi- 
cations for  Steel  Highway  Bridges,  under  Class  B-l. 

NEBRASKA— 300  Ib.  per  lin.ft.  on  the  loaded  chord  and 
150  Ib.  on  the  unloaded  chord. 

OHIO — Same  as  the  Cooper  Specifications,  ed.  of  1909. 

VIRGINIA — 300  Ib.  per  lin.ft.  on  the  loaded  chord,  150  Ib. 
of  which  is  to  be  treated  as  a  moving  load,  and  150  Ib.  per 
lin.ft.  on  the  unloaded  chord. 

MASSACHUSETTS— The  Massachusetts  Railroad  Commis- 
sion, George  F.  Swain,  Consulting  Engineer,  specifies  that,  for 

[  49  ] 


bridges  carrying  electric  railways  "a  lateral  force  of  bO  11).  per 
sq.ft.  on  the  unloaded  structure,  or  of  30  Ib.  per  sq.ft.  on  the 
loaded  structure,  shall  be  provided  for.  The  surface  of  the  un- 
loaded structure  shall,  in  the  case  of  a  truss,  be  taken  as 
twice  the  area  of  the  vertical  elevation  of  one  truss,  plus 
that  of  the  floor;  and  in  the  case  of  a  girder,  as  IS  times  the 
vertical  surface.  The  surface  of  the  loaded  structure  shall 
be  that  of  the  unloaded  structure  plus  a  vertical  surface  10 
ft.  in  height  and  50  ft.  long,  the  pressure  on  which  is  to  be 
considered  a  moving  load  upon  a  car." 

NEW  YORK — The  Department  of  the  State  Engineer  and 
Surveyor  of  New  York  specifies:  "The  intensity  of  the  wind 
pressure  shall  be  assumed  at:  First,  30  Ib.  per  sq.ft.  on  the 
exposed  surface  of  all  railings,  trusses,  trestle  posts,  bracing 
and  the  floor  in  addition  to  a  load  of  150  Ib.  per  lin.ft.  applied 
at  4  ft.  above  the  floor  line  for  all  bridges  which  do  not  carry 
electric  cars,  and  300  Ib.  per  lin.ft.  applied  8  ft.  above  the 
floor  line  for  all  bridges  which  do  carry  electric  cars.  Second, 
50  Ib.  per  sq.ft.  on  all  exposed  surface  of  the  unloaded  struct- 
ure. All  parts  shall  be  proportioned  for  that  one  of  these 
loads  which  gives  the  greater  results,  but  in  no  case  shall 
the  wind  pressure  be  assumed  at  less  than  100  Ib.  per  lin.ft.  at 
the  unloaded  chord,  or  less  than  250  Ib.  per  lin.ft.  at  the 
loaded  chord.  All  wind  loads  shall  be  considered  as  moving- 
loads." 

PHILADELPHIA— The  Department  of  Public  Works  of  the 
City  of  Philadelphia  specifies  for  its  bridges  a  wind  pressure 
of  30  Ib.  per  sq.ft.  against  the  side  area  of  all  trusses,  railings, 
and  the  end  area  of  the  floor  construction.  In  no  case  is  less 
than  150  Ib.  per  lin.ft.  to  be  used.  In  addition  the  system  at- 
tached to  the  floor  is  to  carry  a  moving  load  of  150  Ib.  per 
lin.ft.  of  bridge. 

HARRIMAN  LINES — A  number  of  railway  companies  have 
specifications  for  highway  bridges  attached  to  or  a  part  of 
their  specifications  for  railroad  bridges.  The  Harriman  Lines 
issue  separate  specifications  for  highway  bridges  in  which  the 
wind  pressure  is  taken:  (a)  On  the  loaded  structure  at  30 
Ib.  per  sq.ft.  on  the  exposed  surface  of  all  trusses  and  the 
floor  system  as  seen  in  elevation,  together  with  a  moving  load 
of  150  Ib.  per  lin.ft.  of  bridge,  (b)  On  the  unloaded  struct- 
ure at  50  Ib.  per  sq.ft.  on  the  exposed  surface  taken  as  in  (a). 

U.  S.  ROADS— The  Office  of  Public  Roads,  U.  S.  Depart- 
ment of  Agriculture,  issues  "Typical  Specifications  for  the 
Fabrication  and  Erection  of  Steel  Highway  Bridges."  The  Di- 
rector of  the  Office  states  that  they  are  prepared  "with  the 
view  of  furnishing  a  suitable  guide  for  local  highway  offi- 
cials in  fixing  requirements  to  which  bridge  structures  must 
conform."  He  further  writes,  "In  the  past  many  steel  bridges 
have  been  very  poorly  constructed,  and  it  is  believed  that  lack 
of  information  on  the  part  of  highway  officials  concerning 
proper  specifications  for  this  class  of  work  has  been  in  a  large 
measure  responsible  for  the  unsatisfactory  results."  It  may  be 
remarked  that  unless  the  highway  officials  are  reinforced  by 
competent  engineers,  the  use  of  these  specifications  will  not 
prevent  "unsatisfactory  results."  The  wind  loads  assumed  are 
a  load  of  300  Ib.  per  lin.ft.  on  the  loaded  chord,  one-half  of 

[50] 


this  to  be  treated  as  moving,  and  150  Ib.  per  lin.ft.  on  the  un- 
loaded chord. 

ONTARIO — The  "General  Specifications  for  Steel  Highway 
Bridges,"  of  the  Canadian  province  of  Ontario  are  quite  de- 
tailed in  their  provisions  for  wind  and  lateral  stresses.  For 
Class  A  (bridges  suitable  for  main  county  roads)  in  spans  of 
200  ft.  or  less,  a  uniform  load  of  150  Ib.  per  lin.ft.  per  span  is 
used  on  the  unloaded  chord,  and  the  same  with  the  addition 
of  150  Ib.  per  lin.ft.  moving  load  on  the  loaded  chord;  for 
spans  exceeding  200  ft.  the  uniform  load  in  each  system  is  to 
be  increased  10  Ib.  for  each  30  ft.  of  span.  For  Class  B 
(bridges  carrying  light  rural  traffic),  same  as  Class  A.  For 
Class  C  (bridges  for  heavy  traffic  in  towns  and  cities),  for 
spans  of  200  ft.  and  less,  a  uniform  load  of  200  Ib.  per  lin.ft. 
of  span  on  the  unloaded  chord  and  a  uniform  load  of  250  Ib. 
per  ft.  in  addition  to  a  moving  load  of  250  Ib.  per  ft.  on  the 
unloaded  chord;  for  spans  over  200  ft.  the  uniform  load  in 
each  system  is  to  be  increased  10  Ib.  for  every  30  ft.  increase 
of  span. 

TYRRELL — Merriman  &  Jacoby  in  their  enumeration  of 
noncontinuous  bridges  of  400-ft.  span  and  over  include  21 
which  are  exclusively  highway.  Of  these  21  the  longest  span 
is  that  over  the  Miami  River  at  Elizabethtown,  Ohio  (de- 
stroyed by  flood  in  March,  1913).  This  structure  was  pro- 
portioned "for  a  wind  load  of  30  Ib.  per  sq.ft.  acting  on  the 
exposed  surface  of  both  trusses,  and  all  bracing  that  is  like- 
wise exposed  to  wind  pressure."* 

UNIT-STEESSES 

In  the  specifications  mentioned,  the  values  allowed  for 
stresses  due  to  combined  dead-  and  live-load  and  wind 
are  20  to  30%  greater  than  that  allowed  for  combined 
live-  and  dead-loads.  The  proviso  is  attached  that  the  sec- 
tion used  must  not  be  less  than  that  required  for  the 
combined  dead-  and  live-loads.  One  exception  is  that 
of  the  IT.  S.  Department  of  Agriculture:  these  specifica- 
tions require  that  the  wind  stresses  be  proportioned  with 
the  same  values  as  other  stresses  without  allowance  for 
any  combination  with  other  loads.  This  may  not  be  in- 
tended, but  there  is  no  doubt  of  the  literal  interpretation. 
Another  exception  is  the  Waddell  specifications,  where  in 
highway  bridges  no  reduction  of  working  stress  is  allowed 
for  any  combination  of  loads.  Unless  the  structure  car- 
ries an  electric  railway,  it  is  assumed  that  the  live-load 
and  wind-load  cannot  act  together,  "for  the  reason  that  no 
person  would  venture  on  the  bridge  when  even  one-half 
of  the  assumed  wind-pressure  is  acting." 

*Tyrrell,  The  Elizabethtown  Bridge. 

[51] 


CONCLUSION 

It  will  be  seen  from  the  above  that  the  current  require- 
ments regarding  lateral  bracing  vary  greatly.  A  num- 
ber of  states  have  already  legislated  upon  the  subject  of 
highway  bridges  and  others  will  soon  follow.  As  far  as 
lateral  bracing  is  concerned  it  might  be  well  to  divide 
highway  bridges  into  three  classes,  those  which  carry  elec- 
tric cars,  those  which  carry  heavy  loads  other  than  cars, 
and  ordinary  country  bridges.  A  different  lateral  load- 
ing should  be  assigned  to  spans  over  150  ft.  than  to  those 
under.  It  is  better  to  state  the  wind  pressure  in  pounds 
per  lineal  foot  of  bridge  rather  than  in  pounds  per  square 
foot  of  exposed  surface,  because  contracts  for  highway 
bridges  are  almost  invariably  let  by  competition,  and  if 
wind  loadings  are  given  in  pounds  per  lineal  foot,  the  de- 
signs of  different  bidders  are  on  the  same  basis,  which  may 
not  be  the  case  when  given  in  pounds  per  square  foot. 

After  a  study  of  many  specifications,  the  writer  sug- 
gests the  following : 

RECOMMENDED  SPECIFICATIONS 

For  bridges  carrying-  electric-railway  traffic  the  lateral 
system  shall  be  designed  to  resist  a  lateral  force  of  300  Ib. 
per  lin.ft.  on  the  loaded  chord  and  150  Ib.  per  lin.ft.  on  the 
unloaded  chord,  for  spans  of  150  ft.  and  under.  An  additional 
allowance  of  10  Ib.  for  every  30  ft.  of  span  shall  be  made  to 
the  loaded  chord  and  5  Ib.  to  the  unloaded  chord  for  spans 
of  more  than  150  ft. 

For  bridges  not  carrying  electric  cars,  but  subject  to  heavy 
loads  such  as  auto-trucks,  road  rollers,  and  traction  engines, 
the  lateral  force  shall  be  assumed  at  250  Ib.  per  lin.  ft.  on  the 
loaded  chord  and  150  Ib.  per  lin.ft.  on  the  unloaded  chord,  for 
spans  of  150  ft.  and  under.  An  additional  allowance  of  5  Ib. 
for  every  30  ft.  of  span  shall  be  made  to  each  chord  for  spans 
of  more  than  150  ft. 

Ordinary  country  bridges  shall  be  designed  for  a  lateral 
force  of  225  Ib.  per  lin.ft.  on  the  loaded  chord  and  150  Ib.  on 
the  unloaded  chord  with  an  additional  force  on  the  loaded 
chord  of  5  Ib.  for  every  30  ft.  of  span  exceeding  150  ft. 

All  lateral  loads  are  to  be  considered  as  moving  loads. 

In  members  subject  to  stresses  from  lateral  forces  alone 
the  unit-stresses  may  be  increased  25%  over  those  assumed 
for  live-  and  dead-loads.  In  bridges  carying  electric  cars  the 
unit-stresses  in  chords  and  floor-beams  for  the  stresses  due  to 
lateral  forces  combined  with  those  from  the  vertical  forces 
may  be  increased  25%  over  those  assumed  for  dead-  and  live- 
loads.  If  the  track  is  on  curve  the  centrifugal  force  shall  be 
added  to  the  lateral  live-load.  For  bridges  not  carrying  elec- 
tric traffic,  unit-stresses  of  50%  increase  may  be  used  instead 
of  25%.  In  no  case  shall  the  section  be  less  than  that  re- 
quired for  the  live-  and  dead-loads. 

Provision  shall  be  made  for  reversal  of  stress  in  any  mem- 
ber due  to  any  combination  of  wind  with  other  loads.  The 
end  seats  shall  in  all  cases  be  firmly  anchored  against  lateral 
movement  and  uplift.  In  bridges  in  unusually  exposed  situa- 
tions or  at  a  great  height  above  the  water  the  amount  of 
anchorage  shall  be  determined  by  calculation. 

All  details  shall  be  designed  to  carry  the  stresses  in  the 
main  members. 

[  52  ] 


Wind-Bracing  Requirements  in 
Municipal  Building  Codes 

SYNOPSIS— How  120  American  cities  specify 
wind  pressure  for  the  design  of  buildings.  Great 
range  of  pressures  and  working  stresses.  Recom- 
mendation that  20  Ib.  per  sq.ft.,  and  for  combined 
stress  50%  increase  in  working  stress,  be  adopted 
as  standard. 

The  assumptions  that  are  made  for  wind  pressure  and 
working  stresses  due  to  wind  loads  play  an  important  part 
in  the  design  of  a  many-storied  hotel  or  office  building. 
These  are  seldom  left  to  the  judgment  of  the  designer, 
but  are  determined  by  the  building  code  of  the  city  in 
which  the  building  is  located. 

According  to  the  census  of  1910  there  were  in  the 
United  States  50  cities  each  having  a  population  over 
100,000.  The  building  codes  of  45  of  these  cities,  to- 
gether with  those  of  about  75  cities  below  100,000,  have 
been  examined  with  respect  to  their  requirements  for 
wind  bracing.  The  purpose  of  this  article  is  to  show 
the  wide  variation  in  requirements  in  these  codes,  and  to 
make  a  plea  that  assumptions  be  made  more  nearly  uni- 
form. 

The  present  Building  Code  of  the  City  of  New  York, 
affecting  more  building  operations  than  that  of  any  other 
city  on  the  continent,  was  adopted  in  1899.  The  Board 
of  Aldermen  passed  a  new  code  in  1909,  after  extended 
discussion  and  bitter  controversy,  but  the  Mayor  vetoed 
it.  The  present  code  is  archaic  in  some  of  its  provisions 
and  is  inadequate  for  present  needs.  It  has  been  used 
as  the  basis  for  the  codes  of  a  host  of  other  cities.  Some- 
times it  has  been  copied  with  but  little  change,  and  in 
other  cases  some  sections  have  been  modified  or  rejected. 

Regarding  wind  pressure  the  New  York  code  requires 
that  all  structures  exposed  to  the  wind  (except  those 

[53] 


under  100  ft.  in  height  in  which  the  height  does  not  ex- 
ceed four  times  the  average  width  of  the  base)  be  designed 
to  resist  a  horizontal  wind  pressure  of  30  Ib.  in  any  di- 
rection for  every  square  foot  of  surface  exposed  from  the 
ground  to  the  top,  including  the  roof.  Regarding  unit- 
stresses  the  code  reads : 

In  calculations  for  wind  bracing,  the  working  stresses  set 
forth  in  this  code  may  be  increased  by  50%. 

This  sentence  is  ambiguous  as  it  does  not  state  whether 
the  high  unit-stress  is  applicable  to  the  combined  stresses 
due  to  wind  and  other  loads  or  whether  it  is  to  be  used 
for  the  wind  stress  only.  There  is  considerable  differ- 
ence between  the  two  interpretations  as  to  the  amount  of 
material  required  in  bracing  a  high  and  narrow  building. 
The  Chicago  code  removes  all  doubt  by  specifying: 

For  stresses  produced  by  wind  forces  combined  with  those 
from  live-  and  dead-load,  the  unit-stress  may  be  increased 
50%  over  those  given  above;  but  the  section  shall  not  be 
less  than  that  required  if  wind  forces  be  neglected. 

It  may  be  said  that  the  practice  in  New  York  and  else- 
where is  to  interpret  the  50%  as  applying  to  combined 
stresses. 

Another  sentence  in  the  New  York  code  reads : 

In  all  structures  exposed  to  wind,  if  the  resisting  moments 
of  the  ordinary  materials  of  construction,  such  as  masonry, 
partitions,  floors  and  connections,  are  not  sufficient  to  resist 
the  moment  of  distortion  due  to  wind  pressure,  taken  in  any 
direction  on  any  part  of  the  structure,  additional  bracing 
shall  be  introduced  sufficient  to  make  up  the  difference  in 
the  moments. 

Good  practice  does  not  permit  and  it  is  not  common 
to  carry  the  wind  stresses  in  steel  buildings  either  in  whole 
or  in  part  to  the  ground  by  walls  or  partitions.  The 
Bridgeport  code  has  a  clause  which  should  be  followed, 
reading : 

In  buildings  of  skeleton  construction  the  frame  must  be 
designed  to  resist  this  wind  pressure. 

Manchester,  Albany,  Utica,  Jersey  City,  Paterson,  Terre 
Haute,  Kalamazoo,  Milwaukee,  St.  Paul,  Minneapolis, 
Louisville,  Tampa,  Atlanta,  Dallas  and  Tacoma  all  fol- 
low the  New  York  code  regarding  wind  bracing  except 
for  an  occasional  variation  for  buildings  under  100  ft. 
in  height. 

[54] 


In  Philadelphia  a  pressure  of  not  less  than  30  Ib.  per 
sq.ft.  is  called  for  on  all  buildings  erected  in  open  spaces 
or  on  wharves.  On  tall  buildings  erected  in  built-up 
districts  the  wind  pressure  is  not  to  be  figured  for  less 
than  25  Ib.  at  tenth  story,  2y2  Ib.  IGSS  on  each  succeeding 
lower  story,  and  2%  Ib.  additional  on  each  succeeding 
upper  story  to  a  maximum  of  35  Ib.  at  the  fourteenth 
story  and  above.  In  proportioning  members  subject  to 
stresses  due  to  wind  loads  the  working  stresses  may  be 
increased  30%.  In  Washington  buildings  are  practically 
limited  to  twelve  stories  in  height.  The  prescribed  wind 
pressure  is  the  same  as  in  Philadelphia,  but  no  mention 
is  made  of  any  increase  of  working  stresses.  Lowell, 
Bridgeport,  Baltimore,  Buffalo  and  Sioux  City  assume 
wind  pressure  at  30  Ib.  per  sq.ft.  and  are  also  silent  on 
the  subject  of  working  stresses  being  increased. 

Pittsburgh  calls  for  25  Ib.,  Detroit  and  Jacksonville 
30  Ib.  per  sq.ft.  wind  pressure,  and  each  allows  the  work- 
ing stresses  to  be  increased  25%. 

Cincinnati  requires  provision  to  be  made  for  a  pressure 
of  20  Ib.  per  sq.ft.  for  the  surface  exposed  above  surround- 
ing buildings;  working  stresses  may  be  increased  25%. 
St.  Louis  assumes  a  pressure  of  30  Ib.  per  sq.ft.  and  al- 
lows an  increase  of  20%  to  working  stresses.  The  St. 
Louis  code  has  this  provision : 

"Where  there  are  buildings  immediately  adjoining,  the  wall 
surface  covered  by  such  buildings  will  be  considered  as  not 
exposed  to  wind  pressure. 

The  question  might  be  asked  concerning  buildings  in 
Cincinnati  and  St.  Louis  as  to  what  would  take  the  wind 
pressure  if  the  surrounding  buildings  were  removed. 

Chicago,  San  Francisco,  Covington  and  Akron  call  for 
20  Ib.  per  sq.ft.  wind  pressure.  An  increase  of  50%  to 
the  working  stresses  is  allowed  in  Chicago  and  San  Fran- 
cisco, 25%  in  Covington  and  none  in  Akron. 

Poughkeepsie,  Evansville  and  Chattanooga  call  for  30 
Ib.  per  sq.ft.  horizontal  wind  pressure,  and  state  as  follows : 

The  additional  loads  caused  by  the  wind  pressure  upon 
beams,  girders,  walls  and  columns  must  be  determined  by 
calculation  and  added  to  other  loads  for  such  members. 
Special  bracing  shall  be  employed  wherever  necessary  to 
resist  the  distorting  effect  of  the  wind  pressure. 

[  55  ] 


No  mention  is  made  of  higher  unit-stresses  for  wind 
loads. 

Syracuse,  Erie,  Cleveland,  Duluth,  Denver,  Macon, 
Birmingham  and  Portland  (Oregon)  for  all  buildings 
whose  heights  exceed  1%  times  the  width  of  the  base  fol- 
low the  wind  pressures  given  in  the  Philadelphia  code. 
The  Syracuse  code  alone  allows  an  increase  of  working 
stresses — 25%.  Each  code  has  this  provision: 

Every  panel  in  a  curtain  wall  shall  be  proportioned  to  re- 
sist a  wind  pressure  of  30  Ib.  per  sq.ft. 

The  code  of  Grand  Rapids  copies  the  Schneider  "Spe- 
cifications for  Structural  Work  of  Buildings."  The  wind 
pressure  is  assumed  as  acting  horizontally  in  any  direc- 
tion, as  follows: 

First — At  20  Ib.  per  sq.ft.  on  the  sides  and  ends  of  buildings 
and  on  the  actual  exposed  surface,  or  the  vertical  projection 
of  roofs. 

Second — At  30  Ib.  per  sq.ft.  on  the  total  exposed  surfaces 
of  all  parts  composing  the  metal  framework.  The  framework 
shall  be  considered  an  independent  structure,  without  walls, 
partitions  or  floors. 

For  bracing  and  the  combined  stresses  due  to  wind  and 
other  loading,  the  permissible  working  stresses  may  be 
increased  25%,  or  to  20,000  Ib.  for  direct  compression  or  tension. 

The  code  of  Memphis  has  the  same  provisions  though 
differently  worded. 

The  code  of  Oakland  is  unusually  explicit  in  the  treat- 
ment of  wind  bracing.  For  buildings  of  Class  A  over 
100  ft.  high,  or  where  the  height  exceeds  three  times  the 
least  horizontal  dimension,  or  for  buildings  of  Class  B 
over  80  ft.  high  where  the  height  exceeds  two  times  the 
least  horizontal  dimension,  it  provides : 

The  steel  frame  shall  be  designed  to  resist  a  wind  force  of 
30  Ib.  per  sq.ft.  acting  in  any  direction  upon  the  entire 
exposed  surface.  All  exterior  wall  girders  shall  have  knee- 
brace  connections  to  columns.  Provision  shall  be  made  for 
diagonal,  portal  or  kneebracing  to  resist  wind  stresses,  and 
such  bracing  shall  be  continuous  from  top  story  to  and 
including  basement. 

An  increase  of  50%  above  the  allowed  dead-  and  live-load 
stress  shall  be  used  for  wind  stress.  Columns  subjected  to 
cross-bending  by  wind  or  eccentric  loading  shall  have  addi- 
tional area  to  provide  for  the  stresses,  the  eccentric  loading 
being  calculated  as  dead-load  and  the  wind  provided  above. 
The  area  of  metal  thus  obtained  for  wind,  cross-bending  and 
eccentric  loading  shall  be  added  to  the  area  provided  for 
dead-  and  live-load  to  obtain  the  total  metal  in  column. 

[  56  ] 


In  the  case  of  reinforced-concrete  buildings  where  pro- 
vision must  be  made  for  wind  pressure,  there  is  this  pro- 
vision : 

The  reinforcing  rods  of  columns  shall  be  connected  by 
threading  the  rods  and  by  threaded  sleeve  nuts  or  threaded 
turnbuckles,  or  methods  equally  effective  and  satisfactory  to 
the  Bridge  Inspector. 

In  Salt  Lake  City  for  buildings  over  102  ft.  high,  or 
where  the  height  exceeds  three  times  the  least  horizontal 
dimension,  "the  steel  frame  shall  be  designed  to  resist  a 
wind  force  of  20  Ib.  per  sq.ft.  in  any  direction  upon 
the  entire  exposed  surface."  As  in  Oakland,  it  is  re- 
quired that  the  exterior  wall  girders  shall  have  knee- 
brace  connections  to  the  columns  and  that  diagonal,  por- 
tal or  kneebracing  to  resist  wind  pressure  shall  be  used 
from  the  top  story  to  and  including  basement.  Unlike 
Oakland  no  increase  of  working  stresses  for  wind  loads 
is  mentioned. 

The  code  of  Waltham,  Mass.,  has  the  provision : 

All  buildings  exposed  to  the  wind  shall  be  calculated  to  re- 
sist a  pressure  on  either  side  so  exposed,  and  upon  the  roof,  if 
pitched,  amounting  to  10  Ib.  per  sq.ft.  of  vertical  projection 
of  roof  between  the  ground  and  a  height  of  40  ft.  above 
the  ground,  a  pressure  of  15  Ib.  per  sq.ft.  on  parts  between 
40  and  60  ft.  above  the  ground,  and  20  Ib.  per  sq.ft.  on  parts 
60  ft.  above  the  ground. 

No  increased  working  stresses  for  wind  are  mentioned. 

The  code  of  Columbus,  Ohio,  adopted  ten  years  ago, 
reads  the  same  on  wind  pressure  as  the  New  York  code 
except  that  working  stresses  may  be  increased  25% 
instead  of  50%.  There  is  added  the  sentence: 

In  buildings  constructed  of  structural  steel  the  wind  pres- 
sure shall  be  allowed  for  as  follows:  Ten  Ib.  per  sq.ft.  of  ex- 
posed surface  for  buildings  20  ft.  or  less  to  the  eaves;  20  Ib. 
per  sq.ft.  of  exposed  surface  for  buildings  60  ft.  to  the  eaves; 
30  Ib.  per  sq.ft.  of  exposed  surface  for  buildings  over  60  ft. 
to  the  eaves. 

The  codes  of  Boston,  Cambridge,  Haverhill  and  New 
Orleans  have  the  sentence:  "Provision  for  wind  bracing 
shall  be  made  wherever  it  is  necessary."  This  is  indefin- 
ite and  tends  to  put  a  premium  on  ignorance.  If  all 
designers  were  experts  there  would  still  be  enough  differ- 
ence of  opinion  as  to  the  amount  of  wind  bracing  neces- 
sary. But  a  design  with  little  or  no  wind  bracing  is 
also  entitled  to  consideration  if  the  maker  gives  assur- 

[  67  ] 


ance  that  he  is  furnishing  bracing  "wherever  it  is  neces- 
sary." The  same  might  be  said  concerning  the  codes  of 
New  Haven,  Providence,  Worcester,  Springfield,  Wheel- 
ing, Youngstown,  Toledo,  Omaha,  Lincoln,  Montgomery, 
Fort  Worth,  Los  Angeles  and  others,  which  while  giving 
loads  and  stresses  for  structural  steel  generally  say  noth- 
ing on  the  subject  of  wind  pressure.  Indianapolis  and 
Seattle  allow  an  increase  of  50%  to  the  working  stresses 
but  do  not  state  the  amount  of  pressure. 

The  codes  of  Fall  Eiver,  Pawtucket,  Elizabeth,  Allen- 
town,  Altoona,  Fort  Wayne,  Dubuque  and  Topeka  are 
very  meager  or  altogether  silent  on  the  whole  subject  of 
loads,  stresses,  and  structural  steel. 

Codes  often  contain  blanket  clauses  which  might  be 
used  to  cover  a  wide  range  of  omissions — thus,  Cleveland, 
Duluth,  Little  Eock,  Fort  Worth  and  others  say: 

The  allowable  factor  or  units  of  safety  or  the  dimensions 
of  each  piece  or  combination  of  materials  required  in  a 
building-  or  structure,  if  not  given  in  this  ordinance,  shall 
be  ascertained  by  computation  according  to  the  rules  pre- 
scribed by  the  modern  standard  authorities  on  strength  of 
material,  applied  mechanics  and  engineering  practice. 

Erie,  Pa.,  has  the  sentence:  "In  general  all  stresses 
shall  be  figured  in  accordance  with  the  standard  speci- 
fications of  the  American  Society  of  Civil  Engineers." 

The  New  Haven  code  reads : 

The  dimensions  of  each  piece  or  combination  of  materials 
required  shall  be  ascertained  by  computation  according  to  the 
rules  and  data  given  in  Haswell's  Mechanics'  and  Engineers' 
Pocket  Book,  Trautwine's  Engineers'  Pocket  Book,  or  Kid- 
der's  Architects'  and  Builders'  Pocket  Book,  except  ad  may 
be  otherwise  provided  in  this  title.  Stresses  for  materials 
and  forms  of  same  not  herein  mentioned  shall  be  those 
determined  by  the  best  modern  practice. 

The  last  code  from  which  quotations  will  be  made  is 
that  of  the  largest  city  in  the  world.  The  London  Coun- 
ty Council  (General  Powers)  Act,  1909,  in  Section  22, 
"Provisions  with  respect  to  Buildings  of  Iron  and  Steel 
Skeleton  Construction,"  requires: 

All  buildings  shall  be  so  designed  as  to  resist  safely  a  wind 
pressure  in  any  horizontal  direction  of  not  less  than  30  Ib. 
per  sq.ft.  of  the  upper  two-thirds  of  the  surface  of  such 
buildings  exposed  to  wind  pressure. 

Working  stresses  exceeding  those  specified  "by  not  more 
[  58  ] 


than  25%  may  be  allowed  in  cases  in  which  such  excess 
is  due  to  stresses  induced  by  wind  pressure." 

CONCLUSION 

It  might  seem  from  the  foregoing  that  our  American 
municipalities  have  exhausted  the  combinations  of  wind 
pressure  and  wind  stress  that  can  be  made.  The  fact 
that  one  code  differs  from  another  is  not  in  itself  a  cause 
for  criticism,  but  a  code  is  decidedly  at  fault  when  it 
contains  absurd  or  needless  requirements  or  when  its 
requirements  are  not  clearly  expressed.  To  assume  wind 
pressure  over  a  large  area  at  30  Ib.  per  sq.ft.  and  then 
to  add  the  sectional  area  necessary  to  resist  wind  stresses 
to  that  required  for  live-  and  dead-loads  is  needless. 
Where  this  is  specified  in  a  code  it  is  evaded  in  practice. 
It  would  be  far  better  to  make  rational  assumptions  and 
insist  on  a  rigid  adherence  to  them,  than  to  insert  in  a 
code  improbable  loadings  or  working  stresses  that  will 
be  ignored  in  actual  construction. 

That  the  need  of  revision  in  our  building  codes  is  be- 
ing felt  by  the  public  is  evidenced  by  the  number  now 
being  revised.  Although  our  knowledge  of  wind  action 
is  limited  we  should  be  able  to  come  nearer  to  a  common 
ground  of  requirement  for  wind  bracing  than  we  have  at 
present.  As  a  basis  for  uniformity  the  writer  suggests 
the  building  ordinances  of  Chicago.  The  paragraph  on 
Wind  Eesistance  reads : 

All  buildings  shall  be  designed  to  resist  a  horizontal  wind 
pressure  of  20  Ib.  per  sq.ft.  for  every  square  foot  of  exposed 
surface.  In  no  case  shall  the  overturning  moment  due  to 
wind  pressure  exceed  75%  of  the  moment  of  stability  of  the 
building  due  to  the  dead  load  only. 

The  paragraph  relating  to  Wind  Stress,  previously 
quoted,  reads: 

For  stress  produced  by  wind  forces  combined  with  those 
from  live-  and  dead-loads,  the  unit-stress  may  be  increased 
50%  over  those  given  above;  but  the  section  shall  not  be 
less  than  required  if  wind  forces  be  neglected. 


[59] 


VI 

Windbracing    Without    Diag- 
onals for  Steel-Frame 
Office-Buildings 

SYNOPSIS— Exact  elastic  analysis  of  rigid 
square-panel  tier-building  frames  being  impossible 
in  practice,  approximate  methods  based  on  certain 
arbitrary  assumptions  are  used.  The  first  summar- 
ized statement  of  these  methods  was  given  by  the 
author  in  ENGINEERING  NEWS,  Mar.  13, 1913.  The 
present  article — an  enlarged  revision  of  that  arti- 
cle— gives  four  methods,  and  compares  their  re- 
sults for  a  specific  example.  Method  II-A  of  this 
article  has  been  added,  and  the  treatment  of  the 
other  three  revised  and  corrected. 

If  an  apology  is  needed  for  adding  to  the  literature  of 
the  above  subject,  it  may  be  found  in  the  fact  that  many 
of  the  methods  given  in  technical  papers  for  determining 
stresses  due  to  wind  loadings  are  not  workable.  That 
is,  the  average  engineer  to  whom  falls  the  lot  of  designing 
the  average  office-building  has  neither  the  time  nor 
the  ability  to  handle  the  cumbersome  equations  involved. 
One  paper  published  a  few  years  ago  and  now  before 
the  writer  has  for  its  purpose  "to  develop  the  exact  theory 
of  framework  with  rectangular  panels,  and  then  to  sug- 
gest such  short-cuts  as  may  be  of  use  in  actual  designing/' 
This  is  an  elaborate  paper  in  which  the  theorem  of  four 
moments  is  used.  A  bent  of  two  unequal  bays,  three  col- 
umns and  two  girders,  is  considered  and  by  the  "short- 
cuts" seven  equations  are  found  from  which  the  values 
of  all  the  moments  for  the  floor  in  question  may  be  found. 
Whatever  may  be  the  merit  of  this  and  similar  papers, 
it  has  not  been  recognized  sufficiently  to  be  followed  to 
any  appreciable  extent.  It  is  to  be  regretted  that  the 
treatment  of  the  subject  in  our  textbooks  is  not  more 
complete  and  adequate. 

[61] 


Buildings  like  the  Trinity,  the  Fuller,  the  Singer,  the 
Woolworth,  or  the  Metropolitan  Tower,  in  New  York 
City,  are  each  in  a  class  by  itself,  and  of  necessity  care- 
ful study  is  given  to  the  windbracing.  For  another  and 
a  large  class  of  office-buildings,  little  or  no  attention  is 
given  to  the  matter  of  bracing  for  wind,  either  in  the 
proportioning  of  main  members  or  in  details. 

Without  further  introduction  the  writer  gives  four 
methods  in  current  use  of  calculating  wind  stresses  and 
moments  in  office-buildings  where  diagonals  are  not  per- 
missible. Bach  method  has  its  own  advocates. 

Considering  a  single  bent:  It  will  be  assumed  that  all 
columns  in  any  given  story  have  the  same  sectional  area 
and  the  same  section  modulus,  that  all  girders  of  the  same 
floor  have  the  same  section  modulus,  and  that  the  joints 
are  perfectly  rigid.  It  is  obvious  that  if  the  forces  in 
the  several  members  of  the  frame  are  small  in  relation 
to  the  stiffness  of  the  members,  the  longitudinal  distor- 
tions may  be  neglected;  hence  the  adjacent  joints  oc- 
cupying the  corners  of  a  rectangle  will  after  distortion 
occupy  the  corners  of  an  oblique  parallelogram. 

It  is  assumed  that  the  point  of  contraflexure  of  each 
column  is  at  midheight  of  the  story.  The  first  method 
described  further  involves  the  tacit  assumption  that  the 
girders  have  their  points  of  contraflexure  at  midlength. 
Specific  assumptions  as  to  the  distribution  of  column 
shears  and  direct  stresses  are  made  in  the  several  methods. 
In  only  one  of  the  four  methods  are  the  assumptions 
strictly  consistent.  For  example,  in  Method  I  the  as- 
sumption as  to  location  of  points  of  contraflexure  would 
make  the  distorted  shape  of  panel  constant  in  any  given 
story,  and  from  this  would  follow  that  the  column  shears 
must  be  equal;  but  the  calculation  gives  column  shears 
of  different  amount. 

The  resistance  to  overturning  will  cause  a  direct  stress 
in  tension  on  the  windward  side  of  the  neutral  axis,  taken 
by  all  or  some  of  the  columns  on  that  side  according  to 
the  method  used,  and  a  direct  stress  in  compression  on 
the  leeward  side  taken  by  the  columns  on  that  side. 

Figs.  1,  7,  9,  and  12,  give  results  obtained  from  calcu- 
lations according  to  Methods  I,  II,  II-A  and  III  respec- 

[63] 


tively.  Loads  and  stresses  are  given  in  thousands  of 
pounds  and  bending  moments  in  thousands  of  foot- 
pounds. Direct  stresses  are  given  in  parentheses  (). 

METHOD  I 

This  may  be   called  the   Cantilever   Method   and  is 
a    restatement    with    some    modifications    of    an    arti- 

36  46        3-6  / 

"f 


6.0 


6.0 


fiO 


60' 


(3A) 

(20) 

(0.6) 

12  & 

16  B 

12  6 

(5.1) 

(3.0) 

raa; 

1^ 

0 

O 

O 

(S 

oj 

23-* 

3/2 

^3-# 

(5I) 

(30) 

f^5 

^ 

10 

Y 

>E 

3 

^ 

34.2 

456 

342 

(5.1) 

(3.0) 

(0.9) 

•1 

< 

s 

45  O 

60.0. 

^50 

(5.1) 

(3.0) 

(0.9) 

'   *^ 

*o 

•VJ 

4 

3 

Id 

£53 

744 

55.6 

(5.1) 

(3.0) 

(0.9) 

<VJ 

^ 

« 

^ 

K 

«o 

66  & 

338 

666 

(*•')        ^ 

(3.0) 

F9 

| 

O 

S 

0 

ioao 

1440 

IO80 

(68) 

M 

(,.z) 

\ 

0 

O 

^ 

3 

A                               8 

! 

4«fififL 

A 


.^.jpoa.. 

^' 

is.jaaa. 

,  JV   J^Mfift. 


isr    j  FLOOR  _ 


METHOD       I  tn«  «eW» 

FIG.  1.     EECTANGULAR  BUILDING-FRAME:  DIRECT  AND 

BENDING  STRESSES  CALCULATED  BY  APPROXIMATE 

METHOD  I 

144.0  =  Moment     of     144,000     ft.-lb. 
(4.0)  =  Direct    stress   of   4000   Ib. 


[63  ] 


cle  entitled  "Windbracing  with  Kneebraces  or  Gus- 
set-plates," by  A.  C.  Wilson,  in  The  Engineering  Record, 
Sept.  5,  1908.  A  section  or  bent  of  the  building  is  con- 
sidered similar  to  a  beam  loaded  as  a  cantilever. 

If  a  beam  of  rectangular  section  be  loaded  as  a  cantilever 
with  concentrated  loads,  it  is  possible  by  the  theory  of  flexure 
to  find  the  internal  stresses  at  any  point.  If,  however,  rec- 
tangles be  cut  out  of  the  beam  between  the  loads,  there  will 
then  be  a  different  condition  of  stress.  What  was  the  hori- 
zontal shear  of  the  beam  will  now  be  a  shear  at  the  point  of 
the  contraflexure  of  the  floor  girders,  causing  bending,  and, 
as  in  the  beam,  the  nearer  the  neutral  axis  the  greater  the 
shear.  The  vertical  shear  in  the  beam  would  be  taken  up  by 
the  columns  as  a  shear  at  the  points  of  contraflexure  and  the 
amount  of  this  shear  taken  by  each  column  would,  as  in  the 
beam,  increase  toward  the  neutral  axis.  The  direct  stresses 
of  tension  or  compression  in  the  beam  would  act  on  the  col- 
umns as  a  direct  load  of  either  tension  or  compression,  and 
as  in  the  beam  would  decrease  toward  the  neutral  axis. 

Each  intersection  of  column  with  floor  girders  would  be 
held  in  equilibrium  by  forces  acting  at  the  points  of  contra- 
flexure; and  to  find  all  the  forces  acting  around  a  joint  at  any 
floor  the  bending  moments  of  the  building  at  the  points  of 
contraflexure  of  the  columns  above  and  below  the  floor  in 
question  are  found  as  will  be  explained  later, 

It  is  assumed  that  if  a  beam  of  constant,  symmetrical 
cross-section  and  homogeneous  material  is  fixed  at  both  ends, 
and  that  if  forces  tend  to  move  those  ends  from  a  position 
in  the  same  straight  line  to  a  position  to  one  side  with  the 
ends  still  parallel,  reversed  bending  will  occur  with  the  point 
of  contraflexure  in  the  center  of  the  unsupported  span.  And 
since  this  condition  exists  in  all  columns  and  floor  girders 
it  will  be  necessary  to  find  the  shears  at  the  points  of  con- 
traflexure as  well  as  the  direct  stresses  in  all  members. 


4 ;  7 "FLOOR 


6000 


6V  FLOOR 


5VFLOOR 
t.  \ 

METHOD  I 

FIG.  2.    COLUMN  SHEARS  AND  GIRDER  MOVEMENTS 

AT  SIXTH  FLOOR,  CALCULATED  BY 

METHOD  I 

Fig.  1  gives  stresses  and  maximum  moments  in  all 
members  of  a  section  of  the  building  in  accordance  with 
the  above  statement. 


[  64] 


The  calculation  of  stresses  and  bending  moments  in 
members  about  the  sixth  floor  will  be  given  in  detail.  The 
direct  stress  in  any  column  is  assumed  to  be  proportional 
to  its  distance  from  the  neutral  axis  of  the  cross-section 
of  the  building.  In  the  cross-section  considered,  the 
neutral  axis  coincides  with  the  center  line  of  the  build- 
ing. The  total  moment  of  the  wind  loads  above  the 
sixth  floor  about  the  line  of  inflection  of  the  sixth-story 
columns  must  equal  the  moment  of  the  direct  stresses  in 
these  columns  about  the  neutral  axis.  Let  SX  be  the 
direct  stress  in  each  of  the  sixth-story  columns  B  and  C, 
then  24X  will  be  the  direct  stress  in  each  of  the  sixth- 
story  columns  A  and  D.  Hence  we  have 

(4000  X  30)  +  (6000  X  18)  +  (6000  X  6)  = 
(24X  X  24)  +  (SX  X  8)  +  (8Z  X  8) 

+  (24X  X  24) 
From  which  SX  =  1650  and  24X  =  4950. 

In  the  same  way  for  the  fifth-story  columns  we  have 
the  equation 

(4000  X  42)  +  [6000  X  (30  +  18  +  6)]  = 

[(24X  X  24)  +  (SX  X  8)]  X  2 

From  which  8Z  ==  3075,  the  direct  stress  in  the  fifth- 
story  columns  B  and  (7;  and  24JT  =  9225,  the  direct 
stress  in  the  fifth-story  columns  A  and  D. 

The  total  horizontal  shear  on  any  line  across  the  build- 
ing is  the  sum  of  the  wind  loads  above  that  line.  The 
shear  taken  by  any  column  in  any  story  is  proportional  to 
the  total  horizontal  shear  in  that  story. 

In  Fig.  2,  if  X  =  shear  of  any  fifth-story  column  at 

1  £*  f\r\f\  Q 

its  point  of  inflection,  then  0  '  n    X  or  ^  X  =  shear  at 


point  of  inflection  of  the  sixth-story  length  of  the  same 

6,000    T-         3 

column,  and  ^-7^7:  X  01  ~^  X  =  increment  of  shear 

11 


taken  by  the  column  at  the  floor  girder. 

We  are  now  ready  to  consider  the  forces  about  the  first 
joint,  or  the  intersection  of  Col.  A  with  the  sixth-floor 
girder,  sketched  separately  as  Fig.  3. 

The  difference  between  9225  and  4950  =  4275  is 
taken  up  as  a  shear  in  the  floor  girder  between  Cols. 
A  and  B.  The  moments  of  the  shears  must  hold  the 

[  65  ] 


joint  in  equilibrium.     Taking  moments  about  the  lower 
point  of  inflection  we  have 

(A  ^  X  12)  +  (T3T  X  X  6)  =  4275  X  8 
from  which  X  =  3300,  T8T  X  =  2400  and  T8T  X  =  900. 
The  bending  moment  M±  for  the  floor  girder  is  4275  X  8 
=  34,200  ft.-lb.  The  bending  moment  for  the  fifth- 
story  column  is  3300  X  6  =  19,800  ft.-lb.,  and  that  for 
the  sixth-story  column  is  2400  X  6  =  14,400  ft.-lb.  The 
direct  thrust  on  the  floor  girder  is  6000  —  900  =  5100. 
Proceeding  to  the  second  joint,  sketched  in  Fig.  4 :  The 
difference  between  3075  and  1650  =  1425  acts  as  a 
shear  in  the  girder  between  Cols.  B  and  C.  This  added  to 
the  4275  shear  continued  from  the  girder  between  A  and 
B  makes  a  total  shear  of  5700  in  the  girder.  The  equa- 
tion of  moments  is 

(A  X  X  12)  +  (A  X  X  6)  =  (4275  X  8)  +  (5700  X  8) 
From  which  X  =  7700;    T8T3T  =  5600,  and    T8T  X  = 


5100*" 


FIG.3 


FIG.-4 


3000 


6V  FLOOR  A      (*900) 


3000-j*          900 


FI6.  5 


FIG. 6 


FIGS.  3-6.     SIXTH-FLOOR  JOINTS  OF  BUILDING-FRAME, 
WITH  STRESSES  CORRESPONDING  TO  METHOD  I 


2100,  are  the  shears  taken  by  Col.  B  to  hold  the  joint 
in  equilibrium. 

The  bending  moment  M 2  of  the  girder  from  A  to  B  at 
Col.  B  is  the  same  as  at  Col.  A  with  an  opposite  sign; 
Ms,  of  the  girder  from  B  to  C,  is  5700  X  8  =  45,600 
ft.-lb.  The  bending  moment  of  the  fifth-story  column  is 
7700  X  6  =  46,200  ft.-lb.,  and  that  of  the  sixth-story 
column  is  5600  X  6  =  33,600  ft.-lb.  The  direct  thrust 
on  the  girder  between  B  and  C  is  5100  —  2100  =  3000. 

At  the  third  joint,  Fig.   5,  the  shear  taken  by  the 
girder  between  C  and  D  is  5700  —  (3075  —  1650)  = 
4275.    From  the  equation  of  moments 
(A  X  X  12)  +  (T\  X  X  6)  =  (5700  X  8)  +  (4275  X  8) 
whence 

X  =  7700,  ^  X  =  5600,  ^  X  =  2100 
As  expected,  the  moments  in  Col.  C  are  numerically  equal 
to  those  in  Col.  B,  and  the  girder  moments  M4  =  M&, 
and  M5  =  M2.     The  compression  in  the  floor  girder 
between  C  and  D  is  3000  —  2100  =  900. 

At  the  fourth  joint,  Fig.  6,  we  have 

(T\  X  X  12)  +  (A  X  X  6)  =  (4275  X  8) 
the  same  equation  as  at  the  first  joint,  and  hence  the  same 
numerical  values  for  moments  and  shears. 

The  designer  in  following  this  method  for  the  various 
floors  will  find  many  short-cuts.  A  relationship  between 
the  floors  can  soon  be  established.  If  the  distances  between 
columns  are  not  even  spaces,  or  the  columns  have  differ- 
ent sectional  areas,  the  direct  stresses  vary  both  in  pro- 
portion to  their  distances  from  the  neutral  axis  and  their 
sectional  areas.  It  will  be  necessary  to  first  find  the 
neutral  axis  of  the  cross-section  in  question  and  then  the 
direct  stresses.  With  these  the  shears  and  bending  me 
ments  can  be  obtained. 

METHOD  II 

This  may  be  called  the  Method  of  Equal  Shears.  It  is 
assumed  that  the  horizontal  shear  on  any  plane  is  equally 
distributed  among  the  columns  cut  by  that  plane.  The 
stresses  and  maximum  bending  moments  for  a  cross-sec- 
tion of  the  building  are  as  given  in  Fig.  7. 

[  67  ] 


6-0 


6.0 


6.0 


6.0 


6.0 


$.0 


6.0                         4.0 

6-0                      ROOF 

(30) 

(2.0) 

(1.0) 

A 

21.0 

I4.O 

§ 

§ 
2/.<? 

.8*  jfJ&O*  ^ 

(+5) 

(3.0) 

(,.5) 

39.0 

26.0 

0 

39.0 

T 

(4.5) 

(3.0) 

(1.5) 

J 

I*. 

57.0 

38.0 

0 

a 

q 

57C7 

(VI 

6r-"     Y_FLOOK 

(**J 

(3.0) 

(1.5) 

*^ 

0 

o 

o 

4 

75.0 

50.0 

E) 

75.0 

f 

(4.5) 

(30) 

P? 

I 

MV 

»• 

93.0 

62.0 

0 

0 
93.0 

4C-    V  FLOOK 

(<*.$) 

(*>) 

W) 

} 

>- 
*" 

llt.O 

74.0 

0 

fff.O 

3V    \FLOOK       . 

(4.5) 

130.  0 

(3.0) 
120.0 

q 
vo 

(,.5) 
O 

180.0 

'  A 

1 

(6.0) 

(4.0) 

(2.0) 

1 

I 

5 

I 

O 

1 

<-"^-> 

<....AeV— 

-> 

<-/«^"> 

/V      ty  FLOOR      . 

&  c 

METHOO      H 

FIG.  7.     RECTANGULAR  BUILDING-FRAME:  DIRECT  AND 

BENDING  STRESSES  CALCULATED  BY  APPROXIMATE 

METHOD  II 

120.0     =  Bending  moment  of  120,000  ft.-lb. 
(4.0)    =  Direct  stress  of  4000  Ib. 

Taking  any  aisle  we  find  the  direct  stress  in  the  fifth- 

X  42' 


story  columns  to  be 


\  +  (^,X  30\ 


pf9  X  6) 


16  .  10,^50 


The  direct  stresses  coming  upon  any  interior  column 
[68] 


from  the  adjacent  aisles  are  equal  in  amount  but  op- 
posite in  direction.     Hence  their  algebraic  sum  is  zero 


i  i 

B  C 

METHOD  H 

FIG.  8.    COLUMN-SHEARS  AND  GIRDER  MOMENTS  AT 
SIXTH  FLOOR,  CALCULATED  BY  METHOD  II 

and  only  the  outside  columns  have  direct  stresses.    This 
may  be  found  directly  for  any  story,  say  the  sixth, 
(4000  X  30)  +  (6000  X  18)  +  (6000  X  6) 
divided  by  48  =  5500 

Considering  in  detail,  as  in  Method  I,  the  sixth  floor, 
we  have  in  Fig.  8  the  direct  stresses  and  shears  in  the 
columns. 

The  shear  in  each  girder  is  10,250  -  -  5500  =  4750. 
The  equations  for  bending  moments  in  the  girders  can 
be  written  as  follows : 


M,  =  [(4000  X6)X  (5500X6) 
M3  =  [(4000  X6) +(5500  X6) 
M3  =  [2(4000  X6)  +(5500  X6) 
M4  =  [2(4000X6) +(5500X6) 
M5  =  [3(4000  X6)  +(5500  X6) 
M6  =  [3(4000  X6)  +(5500  X6) 


—[(10,250—5500)  X16 
—[(10,250—5500)  X16 
—[(10,250—5500)  X32 
—[(10,250—5500)  X32 
—[(10,250—5500)  X48 


=  +57,000  ft.-lb. 
=  —19,000  ft.-lb. 
=  +38,000  ft.-lb. 

38,000  ft.-lb. 

=  +19,000  ft.-lb. 
=  —57,000  ft.-lb. 


The  bending  moment  at  the  sixth-floor  girder  of  each 
sixth-story  column  is  4000  X  6  =  24,000  ft.-lb.,  and  of 
each  fifth-story  column  is  5500  X  6  =  33,000  ft.-lb. 

The  compression  in  the  floor  girders  is  6000  —  1500  = 
4500  between  Cols.  A  and  5,  4500  —  1500  =  3000  be- 
tween B  and  C,  and  3000  —  1500  =  1500  between  C 
and  D.  General  equations  can  easily  be  deduced  which 
will  simplify  the  calculation  of  stresses  and  moments  for 
other  floors.  If  the  spaces  between  columns  are  unequal, 
the  direct  stresses  from  adjacent  aisles  will  be  unequal. 
This  difference  is  a  direct  stress  in  the  column  between 
the  two  aisles  considered.  If  the  columns  have  differ- 


[69] 


ent  sectional  areas,  the  horizontal  shear  taken  by  each 
column  will  be  in  proportion  to  its  moment  of  inertia. 

METHOD  II-A 
This  is  a  special  case  of  Method  II  and  may  be  called 

4.0  ROOF 


6.0 


6.0 


6.0 


6.0 


6.0 


6.0 


(333; 

£.0$ 

(0.67) 

> 

14.0 

/4.tf 

140 

(5.0) 

(3.^ 

(1.0) 

1 

fc 

1 

^ 

>• 

^ 

26.0 

26.0 

26.0 

(5.0) 
58.0 

(2.0) 

58.0 

(1.0) 

58.0 

(5.0) 

p.o) 

d.o) 

I 

® 

1 

S 

>- 

50.0 

500 

50.0 

(5.0) 

(5.0) 

d.o) 

s 

* 

1 

1 

>• 

62.0 

6^ 

6^.^7 

(5.0) 

°'^ 

Q.o) 

>- 

74.0 

74.0 

74.0 

(5.0) 

(3-0) 

d.o) 

1 

a 

1 

*3 

/^.<? 

/^^.^ 

120.0 

^.(57; 

C4w; 

0.55) 

"§ 

^ 

§ 

% 

•<-  /6'  -> 

<  /6'  > 

8T-"FLOOR 


^    ^ FLOOR 


y 

__. 


y  • 


^  FLOOR 


7-*  FLOOR 


v  4^ FLOOR 

A~~ 


Y  3^  FLOOR 


v    ^ FLOOR 
^  ^ 


t      .  is  FLOOR 

METHOD  Z-A 

FIG.  9.    EECTANGULAK  BUILDING-FEAME  :    DIRECT  AND 
BENDING  STRESSES  CALCULATED  BY  APPROXI- 
MATE METHOD  II — A 

120.0  =  Bending    moment    of    120,000    ft.-lb. 
(4.0)  =  Direct    stress    of    4000   Ib. 

[70] 


the  Portal  Method.  The  structure  is  regarded  as  equiva- 
lent to  a  series  of  independent  portals.  The  total  hori- 
zontal shear  on  any  plane  is  divided  by  the  number  of 
aisles  instead  of  by  the  number  of  columns  as  in  II.  An 
outer  column  thus  takes  but  one-half  the  shear  of  an  in- 
terior column.  The  stresses  and  maximum  bending  mo- 
ments for  a  cross-section  of  the  building  are  as  given  in 
Fig.  9. 

For  equal  spacing  the  direct  or  vertical  axial  stress  due 
to  the  overturning  moment  of  the  wind  is  all  taken  by  the 
outside  columns  and  is  the  same  in  amount  as  in 
Method  II. 

Considering  in  detail  the  sixth  floor,  we  have  in  Fig.  10 
the  direct  stresses  and  shears  in  the  columns. 

1^  FLOOR 


16000^ 
6000^ 


7,333 


5333 


£333 


£667 
6r*FLOOR 


$,667 


r  SV  FLOOR 


A  B  <_ 

METHOD  3-A 

FIG.  10.     COLUMN-SHEARS  AND  GIRDER  MOMENTS  AT 
SIXTH  FLOOR,  CALCULATED  BY  METHOD  II-A 

The  shear  in  each  girder  is  10,250  --  5500  =  4750. 
The  equations  for  bending  moments  in  the  girders  are  as 
follows : 

Mt  =  [(2,667  X  6)  4-  (3,667  X  6)]  =  438,000 

M,  =  [(2,667  X  6)   4  (3,667  X  6)   —    (10,250  —  5,500)   X  16]  =        —38,000 
M,   =  [(2,667  X  6)   4  (3,667  X  6)    4    (  5,333  X  6)  +  (7,333  X  6) 

—  (10,250  —  5,500)   x  16]  =  4  38,000 
M4  =  [(2,667  X  6)  +  (3,667  X  6)    +    (  5,333  X  6)   4  (7,333  X  6) 

—  (10,250  —  5,500)   X  32]  =  —  38,000 
M,  =  [(2,667  X  6)   4  (3,667  X  6)    4  2(  5,333  X  6)  4-  2(7,333  X  6) 

—  (10,250  —  5,500)   X  321  =  4  38,000 
M6  =  1(2,667  X  6)   4  (3,667  X  6)    +  2(  5,333  X  6)  4  2(7,333  X  6) 

—  (10,250  —  5,500)   X  481  =  —  38.COO 

The  bending  moment  at  the  sixth-floor  girder  of  each 
outer  sixth-story  column  is  2667  X  6  =  16,000  ft.-lb., 
and  of  each  inner  sixth-story  column  is  5333  X  6  = 
32,000  ft.-lb.  At  the  fifth-floor  girder  the  bending  mo- 
ment of  each  fifth-story  outer  column  is  3667  X  6  = 
22,000  ft.-lb.  and  of  each  fifth-story  inner  column  is  7333 
X  6  =  44,000  ft.-lb. 

[71] 


The  compression  in  the  floor  girders  is  6000  —  1000  = 
5000  between  Cols.  A  and  B,  5000  —  2000  =  3000  be- 
tween B  and  C,  and  3000  —  2000  =  1000  between  C 
and  D. 


H      H 


FIG.  11.     CROSS-SECTION  OF  COLUMNS  IN  TRANSVERSE 

BENT 

It  is  noted  from  the  above  that  the  bending  moment  in 
an  outer  column  is  one-half  that  in  an  interior  column; 
that  the  point  of  contraflexure  of  each  girder  is  at  its 
center;  and  the  bending  moments  due  to  wind  for  all 
girders  of  any  transverse  bent  on  the  same  floor  are  alike. 
This  is  an  ideal  condition  for  the  detailer  and  the  shop. 
The  designer  finds  this  method  very  simple  and  his  work 
easily  checked.  The  bending  moment  in  a  girder  is  the 
mean  between  the  bending  moments  in  the  interior  col- 
umn above  and  below  the  girder.  The  width  of  the  aisle 
does  not  affect  the  value  of  the  bending  moment.* 

Methods  I  and  II-A  are  specially  adapted  to  transverse 
bents  when  the  columns  are  turned  as  in  Fig.  11;  also 
when  the  outer  columns  carry  floor  loads  only  and  the 
stresses  are  but  one-half  those  of  the  inner  columns. 

METHOD  III 

This  may  be  called  the  Continuous  Portal  Method.  The 
direct  stresses  in  the  columns  are  assumed  to  vary  as 
their  distances  from  the  neutral  axis,  and  the  horizontal 
shear  on  any  plane  is  equally  distributed  among  the 
columns  cut  by  that  plane.  Stresses  and  maximum  bend- 
ing moments  for  a  cross-section  of  the  building  are  as 
given  in  Fig.  12. 

The  direct  stresses  in  the  columns  are  found  the  same 
way  and  are  the  same  in  amount  as  in  Method  I. 


*Burt,    "Steel    Construction"   Section,   Wind   Bracing. 


Considering  in  detail  the  sixth  floor,  we  have  in  Fig. 
13  the  direct  stresses  and  shears  in  the  columns.  The 
shear  in  the  girder  A  to  B  and  the  girder  C  to  D  is  9225 
—  4950  =  4275.  The  shear  in  the  girder  B  to  C  is 
(9225  —  4950)  +  (3075  —  1650)  =  5700. 


4.0 


6.0 


6.0' 


6.0 


6.0 


6.0 


6.0- 


8.0' 


6.0 


•48 


6.0 


(3.0) 

(2.0) 

M 

•5f 

^f\ 

q 

o 

| 

£ 

o 

^O 

21.0 

16.8 

zt.o 

(4.5) 

(3.0) 

(1.5) 

s 

£ 

Q 

uj 

39.0 

3I.Z 

390 

(4.5) 

(3.0) 

(l.5) 

? 

1 

s 

0 

57.0 

45.6 

57.O 

75.0 

(3.0) 

(1.5) 

£s 

0 

^ 

O 

K 

600 

75O 

(45) 

0 

(f.5) 

"^ 

^S 

6 

V 

<VJ 

93.0 

93.0 

(4.5) 

(30) 

(1.5) 

^0 

K- 

0 

O 

s<\3 

K 

«5 

«H 

tt/.O 

88.8 

l/t.O 

180.0 

(3.0) 

(>•*) 

""^T 

Ci 

o 

i 

i 

t 

/44.O 

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(4.0) 

(2.0) 

o 

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<-.-,&'-o'~- 

s 

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Jg°V    ^ 


2±.)LJ5WaL. 

^ 


METHOD     Ht 

FIG.  12.    EECTANGULAR  BUILDING-FEAME  :  DIEECT  AND 

BENDING  STRESSES  CALCULATED  BY  APPROXIMATE 

METHOD  III 

144.0  =  Bending  moment  of  144,000  ft.-lb. 
(4.0)   =  Direct  stress  of  4000  Ib. 


The  equations  for  bending  moments  in  the  girders  can 
be  written  as  follows : 

Mj  =     [(4000  X6) +(5500  X6)   =  +57,000  ft.-lb. 

M,  =     [(4000X6)  +(5500X6)1— [(9225^950)  X16]  =  —11,400  ft.-lb. 

M,  =  2[(4000X6) +(5500X6)]— [(9225— 4950)  X 16]  =  +45,600  ft.-lb. 

2[(4000X6)  +(5500X6)]— [(9225-^950)  X32]— [(3075— 1650)  X16]  = 

— 45,600  ft.-lb. 

3[(4000X6)  +(5500X6)]— [(9225— 4950)  X32]— [(3075— 1650)  X16]  = 

+  11,400  ft.-lb 


& 

M8 

B. 


3[(4000X6)  +(5500X6)]— [(9225— 4950)  X48]— [(3075— 1650)  X32]  + 
[(3075—1650)  X16]  =  —57,000  ft.-lb. 

The  bending  moment  at  the  six-floor  girder  of  each 
sixth-story  column  is  4000  X  6  =  24,000  ft.-lb.,  and  of 


6000 


5500    § 
to 


7*  FLOOR 


6  r-«  FLOOR 


•A 


i 

«B  1C 

METHOD  3H 


& 


fvnoo* 
!D 


FIG.  13.    COLUMN-SHEARS  AND  GIRDER  MOMENTS  AT 
SIXTH  FLOOR,  CALCULATED  BY  METHOD  III 

each  fifth-story  column  is  5500  X  6  =  33,000  ft.-lb.  The 
compression  in  the  floor  girders  is  6000  —  1500  = 
4500  Ib.  between  Cols.  A.  and  B,  4500  —  1500  =  3000 
between  B  and  C,  and  3000  —  1500  =  1500  between  C 
and  D. 

If  the  columns  are  unequally  spaced  or  their  sectional 


LOAD  JUV£&DZAD) 


6VFLOOR 


FIG.  14.    GRAPHICAL  COMBINATION  OF  MOMENTS  FROM 

VERTICAL  LOADS  AND  WIND  LOADS  IN  FLOOR 

GIRDER 

areas  are  different,  the  location  of  the  neutral  axis  must 
first  be  found.  The  direct  stresses  in  the  columns  will 
vary  both  as  their  distances  from  the  neutral  axis  and 

[  M] 


their  sectional  areas.    The  horizontal  shears  taken  by  the 
columns  will  vary  as  their  moments  of  inertia. 

CONCLUSION 

It  can  be  said  of  each  of  the  above  methods  of  calculat- 
ing wind  stresses  that  it  is  easily  workable;  and  to  quote 
Prof.  W.  H.  Burr :  "So  long  as  the  stresses  found  by  one 
legitimate  method  of  analysis  are  provided  for,  the  sta- 
bility of  the  structure  is  assured."  At  the  present  time 
Method  I  is  probably  more  used  than  any  of  the  others, 
though  Methods  II  and  II-A  have  been  used  quite  exten- 
sively. In  the  36-story  Equitable  Building  of  New  York 
City,  the  largest  office  building  in  the  world,  Method  I 
was  followed.  In  its  near  neighbor,  the  32-story  Adams 
Express  Building,  Method  II-A  was  used.  Method  III 
is  found  in  some  text-books;  it  has  been  used  but  little 
about  New  York,  and  only  to  a  limited  extent  elsewhere. 
The  writer  personally  prefers  Method  I,  though  during 
the  past  ten  years  he  has  used  I,  II,  and  II-A.  In  a  20- 
story  building  in  Philadelphia  built  in  1914-1915  he  used 
I.  In  an  18-story  building  in  Atlanta,  designed  in  1912, 
he  used  II-A.  To  Method  III  he  objects  not  only  because 
of  its  practical  limitations  but  because  in  theory  it  seems 
farther  from  the  truth  than  any  of  the  others — especially 
when  it  comes  to  distributing  the  shear  for  bents  in  build- 
ings more  than  four  aisles  wide. 

The  practice  of  the  writer  in  calculating  wind  stresses, 
using  Methods  I  or  II-A  (preferably  I),  is  first  to  find 
the  distance  of  each  column  from  the  neutral  axis  of  the 
transverse  bent  to  which  it  belongs,  and  then  to  assume 
the  moments  of  inertia  of  the  inner  columns  in  that  bent 
to  be  the  same  and  of  the  outer  columns  to  be  one-half 
that  of  the  inner.  The  columns  are  proportioned  for  all 
stresses  coming  upon  them,  including  both  direct  and 
cross-bending  due  to  wind.  It  is  seldom  that  corrections 
are  made  for  moments  of  inertia  that  differ  from  the  as- 
sumptions. 

It  is  often  convenient  to  assume  the  wind  loads  on  the 
basis  of  using  the  same  unit-stresses  as  for  live-  and  dead- 
loads.  A  number  of  building  codes  call  for  a  horizontal 
wind  pressure  of  30  Ib.  per  sq.ft.  and  allow  unit-stresses 

[75  ] 


to  be  increased  50%  for  wind-bracing.  A  wind  load  of  30 
Ib.  per  sq.ft.  with  unit-stress  of  24,000  Ib.  per  sq.in.  is 
equivalent  to  a  load  of  20  Ib.  per  sq.ft.  with  a  unit-stress 
of  16,000  Ib.  per  sq.in. — the  working  stress  generally  used 
for  live-  and  dead-loads.  The  diagrams  of  moments  for 
any  floor  girder  can  easily  be  combined  in  one  figure  (see 
Fig.  14),  and  the  total  moment  at  any  point  read  by  scal- 
ing. Fig.  14  is  drawn  for  beam  with  ends  supported.  If 
the  ends  were  considered  fixed  the  beam  would  be  re- 
strained and  the  diagram  for  both  wind  and  floor  loads 
would  show  smaller  bending  moments.  Any  saving  thus 
made  is  doubtful  economy  as  in  actual  practice  it  is  un- 
certain to  what  extent  the  beams  are  fixed  (under  vertical 
load). 

The  building  should  be  examined  for  wind  in  a  longi- 
tudinal direction  as  well  as  transversely  and  calculations 
made  if  necessary.  This  is  a  simple  thing  to  do  but  in 
some  marked  instances  it  has  been  neglected. 

Special  attention  should  be  given  the  column  splices, 
and  the  connection  of  floor  girders  to  columns.  It  is  folly 
to  add  material  to  columns  or  floor  girders  to  meet  stresses 
and  moments  due  to  wind,  and  then  neglect  their  connec- 
tions. Care  should  be  taken  that  in  all  cases  the  connec- 
tions are  made  strong  enough  for  the  bending  moments 
coming  upon  them.  Many  buildings  have  main  members 
sufficient  to  meet  wind  stresses  without  efficient  connec- 
tions. In  such  cases  it  matters  little  what  particular 
theory  of  wind  distribution  had  been  adopted. 


[  70 


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OF  CALIFORNIA  LIBRARY 


